https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Bboggess&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-28T12:54:30ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020/Abstracts&diff=19931NTSGrad Fall 2020/Abstracts2020-09-22T17:59:31Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2020|here.]]<br />
<br />
<br />
== Sep 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Local Arithmetic Siegel-Weil Formula at Ramified Prime''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe a local arithmetic Siegel-Weil formula which relates certain intersection number on U(1,1) Rapoport-Zink space with local density. Via p-adic uniformization, this can be used to establish a global Siegel-Weil formula. The main novelty of this work is that we consider the ramified case. This is a joint work with Yousheng Shi and Tonghai Yang.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnny Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Bounding Numbers Fields up to Discriminant''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
For those interested in arithmetic statistics, I'll present a quick proof of Schmidt's bound on numbers fields of given degree and bounded discriminant, as well as giving a quick overview of recent improvements on this bound by Ellenberg and Venkatesh. <br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020/Abstracts&diff=19930NTSGrad Fall 2020/Abstracts2020-09-22T17:59:18Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2020|here.]]<br />
<br />
<br />
== Sep 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Local Arithmetic Siegel-Weil Formula at Ramified Prime''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe a local arithmetic Siegel-Weil formula which relates certain intersection number on U(1,1) Rapoport-Zink space with local density. Via p-adic uniformization, this can be used to establish a global Siegel-Weil formula. The main novelty of this work is that we consider the ramified case. This is a joint work with Yousheng Shi and Tonghai Yang.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnny Han''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Bounding Numbers Fields up to Discriminant''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
For those interested in arithmetic statistics, I'll present a quick proof of Schmidt's bound on numbers fields of given degree and bounded discriminant, as well as giving a quick overview of recent improvements on this bound by Ellenberg and Venkatesh. <br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020&diff=19929NTSGrad Fall 20202020-09-22T17:58:34Z<p>Bboggess: /* Fall 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' https://uwmadison.zoom.us/j/92879430953<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Fall 2020 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall 2020/Abstracts#Sep_15|Local Arithmetic Siegel-Weil Formula at Ramified Prime]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Johnny Han<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2020/Abstracts#Sep_22|Bounding Numbers Fields up to Discriminant]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Brandon Boggess<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 6th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 13th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 20th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 27th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Peter Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Owen Goff<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Jiaqi Hou<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Tejasi Bhatnagar<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Hyun Jong Kim (hyunjong.kim@math.wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Soumya Sankar<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Fall 2019 is [[NTSGrad_Fall_2019|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020/Abstracts&diff=19816NTSGrad Fall 2020/Abstracts2020-09-15T14:16:51Z<p>Bboggess: Created page with "This page contains the titles and abstracts for talks scheduled in the Fall 2020 semester. To go back to the main GNTS page, click here. == Sep 15 ==..."</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2020|here.]]<br />
<br />
<br />
== Sep 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Local Arithmetic Siegel-Weil Formula at Ramified Prime''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe a local arithmetic Siegel-Weil formula which relates certain intersection number on U(1,1) Rapoport-Zink space with local density. Via p-adic uniformization, this can be used to establish a global Siegel-Weil formula. The main novelty of this work is that we consider the ramified case. This is a joint work with Yousheng Shi and Tonghai Yang.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020&diff=19815NTSGrad Fall 20202020-09-15T14:15:43Z<p>Bboggess: /* Fall 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' https://uwmadison.zoom.us/j/92879430953<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Fall 2020 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall 2020/Abstracts#Sep_15|Local Arithmetic Siegel-Weil Formula at Ramified Prime]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 6th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 13th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 20th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 27th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| Probably Thanksgiving or something<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Hyun Jong Kim (hyunjong.kim@math.wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Soumya Sankar<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Fall 2019 is [[NTSGrad_Fall_2019|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Main_Page&diff=19814Main Page2020-09-15T14:14:12Z<p>Bboggess: /* Graduate Student Seminars */</p>
<hr />
<div><br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources. Pages can only be edited by members of the department but are viewable by everyone. <br />
<br />
*[[Getting Around Van Vleck]]<br />
<br />
*[[Computer Help]] <br />
<br />
*[[Connecting/Using our research servers]]<br />
<br />
*[[Graduate Student Guide]]<br />
<br />
*[[Teaching Resources]]<br />
<br />
== Research groups at UW-Madison ==<br />
<br />
*[[Algebra]]<br />
*[[Analysis]]<br />
*[[Applied|Applied Mathematics]]<br />
*[https://www.math.wisc.edu/wiki/index.php/Research_at_UW-Madison_in_DifferentialEquations Differential Equations]<br />
*[[Dynamics Special Lecture]]<br />
*[[Geometry and Topology]]<br />
* [http://www.math.wisc.edu/~lempp/logic.html Logic]<br />
*[[Probability]]<br />
<br />
== Math Seminars at UW-Madison ==<br />
<br />
*[[Colloquia|Colloquium]]<br />
*[[Algebra_and_Algebraic_Geometry_Seminar|Algebra and Algebraic Geometry Seminar]]<br />
*[[Analysis_Seminar|Analysis Seminar]]<br />
*[[Applied/ACMS|Applied and Computational Math Seminar]]<br />
*[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar_Spring_2020 Applied Algebra Seminar]<br />
*[[Cookie_seminar|Cookie Seminar]]<br />
*[[Geometry_and_Topology_Seminar|Geometry and Topology Seminar]]<br />
*[[Group_Theory_Seminar|Group Theory Seminar]]<br />
*[[Matroids_seminar|Matroids seminar]]<br />
*[[Networks_Seminar|Networks Seminar]]<br />
*[[NTS|Number Theory Seminar]]<br />
*[[PDE_Geometric_Analysis_seminar| PDE and Geometric Analysis Seminar]]<br />
*[[Probability_Seminar|Probability Seminar]]<br />
* [http://www.math.wisc.edu/~lempp/conf/swlc.html Southern Wisconsin Logic Colloquium]<br />
*[[Research Recruitment Seminar]]<br />
<br />
=== Graduate Student Seminars ===<br />
<br />
*[[AMS_Student_Chapter_Seminar|AMS Student Chapter Seminar]]<br />
*[[Graduate_Algebraic_Geometry_Seminar|Graduate Algebraic Geometry Seminar]]<br />
*[[Graduate_Applied_Algebra_Seminar|Graduate Applied Algebra Seminar]]<br />
*[[Applied/GPS| GPS Applied Math Seminar]]<br />
*[[NTSGrad_Fall_2020|Graduate Number Theory/Representation Theory Seminar]]<br />
*[[Symplectic_Geometry_Seminar|Symplectic Geometry Seminar]]<br />
*[[Math843Seminar| Math 843 Homework Seminar]]<br />
*[[Graduate_student_reading_seminar|Graduate Probability Reading Seminar]]<br />
*[[Summer_stacks|Summer 2012 Stacks Reading Group]]<br />
*[[Graduate_Student_Singularity_Theory]]<br />
*[[Graduate/Postdoc Topology and Singularities Seminar]]<br />
*[[Shimura Varieties Reading Group]]<br />
*[[Summer graduate harmonic analysis seminar]]<br />
*[[Graduate Logic Seminar]]<br />
*[[SIAM Student Chapter Seminar]]<br />
*[[Summer 2019 Algebraic Geometry Reading Group]]<br />
*[[CCA Reading Group]]<br />
<br />
=== Other ===<br />
*[https://sites.google.com/site/uwmadisondrp/home Directed Reading Program]<br />
*[[Madison Math Circle]]<br />
*[[High School Math Night]]<br />
*[http://www.siam-uw.org/ UW-Madison SIAM Student Chapter]<br />
*[http://www.math.wisc.edu/%7Emathclub/ UW-Madison Math Club]<br />
*[[Putnam Club]]<br />
*[[Undergraduate Math Competition]]<br />
*[[Basic Linux Seminar]]<br />
*[[Basic HTML Seminar]]<br />
<br />
== Graduate Program ==<br />
<br />
* [[Algebra Qualifying Exam]]<br />
* [[Analysis Qualifying Exam]]<br />
* [[Topology Qualifying Exam]]<br />
<br />
== Undergraduate Program ==<br />
<br />
* [[Overview of the undergraduate math program|Overview]]<br />
* [[Groups looking to hire students as tutors]]<br />
<br />
== Getting started with Wiki-stuff ==<br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020&diff=19813NTSGrad Fall 20202020-09-15T14:13:25Z<p>Bboggess: </p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' https://uwmadison.zoom.us/j/92879430953<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Fall 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 6th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 13th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 20th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 27th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| Probably Thanksgiving or something<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Hyun Jong Kim (hyunjong.kim@math.wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Soumya Sankar<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Fall 2019 is [[NTSGrad_Fall_2019|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=19812NTSGrad Fall 20192020-09-15T14:12:51Z<p>Bboggess: </p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Fall 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_12| Tate's Thesis and Rankin-Selberg theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_19| Cohomology Juggle]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Dec_3| A brief introduction to the Bloch-Kato conjecture and motivic cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
The seminar webpage for Fall 2020 is [[NTSGrad_Fall_2020|here]].<br><br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2020&diff=19811NTSGrad Fall 20202020-09-15T14:12:39Z<p>Bboggess: Created page with "= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison = *'''When:''' Tuesdays, 2:30 PM – 3:30 PM *'''Where:''' https://uwm..."</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' [[https://uwmadison.zoom.us/j/92879430953|Zoom]]<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Fall 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 6th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 13th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 20th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 27th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| Probably Thanksgiving or something<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| <br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Hyun Jong Kim (hyunjong.kim@math.wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Soumya Sankar<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Fall 2019 is [[NTSGrad_Fall_2019|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=19353NTSGrad Spring 2020/Abstracts2020-04-13T13:59:09Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt and John Yin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Golomb Topologies and Infinitely Many Irreducibles''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1955, Furstenberg gave a proof of the infinitude of primes by imposing a topology on Z. Under this topology, all open sets are infinite, but if you assume only finitely many primes then {1} is open. A new, similar, topology was introduced by Golomb in 1959, which turned Z^+ into a connected Hausdorff space. A general Golomb topology on a domain R was introduced by Knopfmacher and Porubský in 1997. I will draw on a paper of Clark, Lebowitz-Lockard, and Pollack, and discuss interesting properties of these topologies, and how they relate to properties of the domain R.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Perspectives on Rational Points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is going to be an all-you-can-eat smorgasbord of techniques for finding rational points on curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Squares in Arithmetic Progressions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will see how results about rational points on curves can say something about integers in arithmetic progressions.<br />
<br />
[[Media:mar_24_slides.pdf | Slides]]<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 31 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''A1 Homotopy Degree''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Morel and Voevodsky's A1 Homotopy Theory (c. 1998-1999) develops a homotopy theory for algebraic geometry that is analogous to the more familiar homotopy theory from algebraic topology - here, the unit interval [0,1] is replaced with the affine line A1. One concept that emerges from Morel and Voevodsky's theory is A1 Homotopy Degree, which can be defined for maps from the A1 homotopy sphere to itself. I will focus on how to compute the A1 Homotopy Degrees of such maps in a nice case, which is tractable due to work by Kass and Wickelgren (2016).<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | '' An introduction to l-adic Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The goal of this talk is to introduce l-aidc Galois representations in various aspects, mostly related to the ones appearing in geometry through l-aidc étale cohomology of varieties. I will focus on Galois representations in two cases, finite fields and local fields.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=19352NTSGrad Spring 20202020-04-13T13:57:04Z<p>Bboggess: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Online, at Webex<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon.<br />
<br />
= Spring 2020 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_4| ABC’s of Shimura Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://will-hardt.com/ Will Hardt] and John Yin<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_11| Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_25| Golomb Topologies and Infinitely Many Irreducibles]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_3 | Perspectives on Rational Points]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_24 | Squares in Arithmetic Progressions]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_31 | A1 Homotopy Degree]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Spring 2020/Abstracts#Apr_7 | An Introduction to l-adic Galois Representations]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=19306NTSGrad Spring 2020/Abstracts2020-03-25T15:49:06Z<p>Bboggess: /* Mar 24 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt and John Yin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Golomb Topologies and Infinitely Many Irreducibles''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1955, Furstenberg gave a proof of the infinitude of primes by imposing a topology on Z. Under this topology, all open sets are infinite, but if you assume only finitely many primes then {1} is open. A new, similar, topology was introduced by Golomb in 1959, which turned Z^+ into a connected Hausdorff space. A general Golomb topology on a domain R was introduced by Knopfmacher and Porubský in 1997. I will draw on a paper of Clark, Lebowitz-Lockard, and Pollack, and discuss interesting properties of these topologies, and how they relate to properties of the domain R.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Perspectives on Rational Points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is going to be an all-you-can-eat smorgasbord of techniques for finding rational points on curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Squares in Arithmetic Progressions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will see how results about rational points on curves can say something about integers in arithmetic progressions.<br />
<br />
[[Media:mar_24_slides.pdf | Slides]]<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=19305NTSGrad Spring 2020/Abstracts2020-03-25T15:48:33Z<p>Bboggess: /* Mar 24 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt and John Yin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Golomb Topologies and Infinitely Many Irreducibles''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1955, Furstenberg gave a proof of the infinitude of primes by imposing a topology on Z. Under this topology, all open sets are infinite, but if you assume only finitely many primes then {1} is open. A new, similar, topology was introduced by Golomb in 1959, which turned Z^+ into a connected Hausdorff space. A general Golomb topology on a domain R was introduced by Knopfmacher and Porubský in 1997. I will draw on a paper of Clark, Lebowitz-Lockard, and Pollack, and discuss interesting properties of these topologies, and how they relate to properties of the domain R.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Perspectives on Rational Points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is going to be an all-you-can-eat smorgasbord of techniques for finding rational points on curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Squares in Arithmetic Progressions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will see how results about rational points on curves can say something about integers in arithmetic progressions.<br />
[[Media:mar_24_slides.pdf]]<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=File:Mar_24_slides.pdf&diff=19304File:Mar 24 slides.pdf2020-03-25T15:47:40Z<p>Bboggess: Slides from GNTS on March 24</p>
<hr />
<div>Slides from GNTS on March 24</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=19293NTSGrad Spring 2020/Abstracts2020-03-23T15:14:33Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt and John Yin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Golomb Topologies and Infinitely Many Irreducibles''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1955, Furstenberg gave a proof of the infinitude of primes by imposing a topology on Z. Under this topology, all open sets are infinite, but if you assume only finitely many primes then {1} is open. A new, similar, topology was introduced by Golomb in 1959, which turned Z^+ into a connected Hausdorff space. A general Golomb topology on a domain R was introduced by Knopfmacher and Porubský in 1997. I will draw on a paper of Clark, Lebowitz-Lockard, and Pollack, and discuss interesting properties of these topologies, and how they relate to properties of the domain R.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Perspectives on Rational Points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is going to be an all-you-can-eat smorgasbord of techniques for finding rational points on curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Squares in Arithmetic Progressions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will see how results about rational points on curves can say something about integers in arithmetic progressions.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=19292NTSGrad Spring 20202020-03-23T15:13:12Z<p>Bboggess: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Online, at Webex<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon.<br />
<br />
= Spring 2020 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_4| ABC’s of Shimura Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://will-hardt.com/ Will Hardt] and John Yin<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_11| Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_25| Golomb Topologies and Infinitely Many Irreducibles]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_3 | Perspectives on Rational Points]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_24 | Squares in Arithmetic Progressions]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=19291NTSGrad Spring 20202020-03-23T15:10:01Z<p>Bboggess: /* Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Online, at Webex<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon.<br />
<br />
= Spring 2020 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_4| ABC’s of Shimura Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://will-hardt.com/ Will Hardt] and John Yin<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_11| Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_25| Golomb Topologies and Infinitely Many Irreducibles]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_3 | Perspectives on Rational Points]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=19178NTSGrad Spring 2020/Abstracts2020-03-02T17:33:24Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt and John Yin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Golomb Topologies and Infinitely Many Irreducibles''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1955, Furstenberg gave a proof of the infinitude of primes by imposing a topology on Z. Under this topology, all open sets are infinite, but if you assume only finitely many primes then {1} is open. A new, similar, topology was introduced by Golomb in 1959, which turned Z^+ into a connected Hausdorff space. A general Golomb topology on a domain R was introduced by Knopfmacher and Porubský in 1997. I will draw on a paper of Clark, Lebowitz-Lockard, and Pollack, and discuss interesting properties of these topologies, and how they relate to properties of the domain R.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Perspectives on Rational Points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is going to be an all-you-can-eat smorgasbord of techniques for finding rational points on curves.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=19177NTSGrad Spring 20202020-03-02T17:31:33Z<p>Bboggess: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_4| ABC’s of Shimura Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://will-hardt.com/ Will Hardt] and John Yin<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_11| Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_25| Golomb Topologies and Infinitely Many Irreducibles]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Mar_3 | Perspectives on Rational Points]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18389NTSGrad Fall 20192019-11-11T18:10:03Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_12| Tate's Thesis and Rankin-Selberg theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18388NTSGrad Fall 2019/Abstracts2019-11-11T18:09:23Z<p>Bboggess: /* Nov 12 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><br />
<br><br />
<br />
== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><br />
<br><br />
<br />
== Oct 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Artin-Hecke <math>L</math>-functions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to Artin-Hecke <math>L</math>-functions, their basic algebraic and analytic properties, and “equivalence” via class field theory. If time permits, I will briefly introduce what the Rankin-Selberg <math>L</math>-function is and what it’s meant for.<br />
|} <br />
</center><br />
<br><br />
<br />
== Nov 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Tate's Thesis and Rankin-Selberg theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Yang's talk at the number theory seminar is related to Tate's thesis and Rankin-Selberg theory, so I'm going to introduce both. Tate's thesis generalizes the functional equation of the Riemann zeta function to a function defined using the adeles. Furthermore, the Rankin-Selberg method uncovers a functional equation for an L-function. I will focus on the classical Rankin-Selberg method, but I may also be able to talk about adelic Rankin-Selberg, which seems to be good to know for Yang's talk.<br />
|} <br />
</center><br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18387NTSGrad Fall 2019/Abstracts2019-11-11T18:08:59Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><br />
<br><br />
<br />
== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><br />
<br><br />
<br />
== Oct 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Artin-Hecke <math>L</math>-functions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to Artin-Hecke <math>L</math>-functions, their basic algebraic and analytic properties, and “equivalence” via class field theory. If time permits, I will briefly introduce what the Rankin-Selberg <math>L</math>-function is and what it’s meant for.<br />
|} <br />
</center><br />
<br><br />
<br />
== Nov 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Tate's Thesis and Rankin-Selberg theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Yang's talk at the number theory seminar is related to Tate's thesis and Rankin-Selberg theory, so I'm going to introduce both. Tate's thesis generalizes the functional equation of the Riemann zeta function to a function defined using the adeles. Furthermore, the Rankin-Selberg method uncovers a functional equation for an L-function. I will focus on the classical Rankin-Selberg method, but I may also be able to talk about adelic Rankin-Selberg, which seems to be good to know for Yang's talk.<br />
|} <br />
</center><br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18171NTSGrad Fall 2019/Abstracts2019-10-14T18:26:52Z<p>Bboggess: /* Oct 7 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18170NTSGrad Fall 2019/Abstracts2019-10-14T18:26:44Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18169NTSGrad Fall 20192019-10-14T18:25:52Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18069NTSGrad Fall 2019/Abstracts2019-10-01T18:14:33Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18068NTSGrad Fall 20192019-10-01T18:13:18Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=17896NTSGrad Fall 2019/Abstracts2019-09-16T16:15:53Z<p>Bboggess: /* Sept 17 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=17895NTSGrad Fall 2019/Abstracts2019-09-16T16:15:42Z<p>Bboggess: /* Sept 10 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula'''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=17894NTSGrad Fall 2019/Abstracts2019-09-16T16:15:14Z<p>Bboggess: /* Sept 10 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields'''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula'''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=17893NTSGrad Fall 20192019-09-16T16:14:21Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| TBA<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17672NTSGrad Spring 2019/Abstracts2019-08-26T16:01:27Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD thesis. I will try my best to make this talk completely self-contained, i.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 2 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Weitong Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On <math>\ell</math>-torsion in class groups of number fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
According to Wei-Lun's request, I'll first introduce the big picture of the paper Nonvanishing of Hecke L-Functions and Bloch-Kato <math>p</math>-Selmer Groups, then focus on the quadratic case of the <math>\ell</math>-torsion in class groups.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 9 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sang Yup Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I’ll attempt to provide a number theorist’s explanation of flows and ergodicity, using one of our favorite spaces as an example. Then I’ll motivate the subject by presenting Sarnak’s conjecture on the randomness of the Mobius function and it’s corollaries.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Apr 16 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Niudun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The march towards Malle's Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will introduce Malle's conjecture and what is known about it. Then I will present an example using the most complicated group, <math>\mathbb{Z}/2\mathbb{Z}</math> to show how we count things in practice.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 23 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Insufficiency of the Brauer Manin obstruction''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will sketch an example of Poonen showing that the Brauer-Manin obstruction is insufficient in general to detect the non existence of rational points.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 30 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Cohen-Lenstra Heuristics''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I will give a brief introduction to the Cohen-Lenstra Heuristics and will talk about how taking a rank n <math>\mathbb{Z}_p</math> module with random relations with respect to the Haar measure gives the Cohen- Lenstra distribution on finite abelian groups for class groups of imaginary quadratic fields.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== May 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Stacky Curves and the Generalized Fermat Equation''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
We will look at the generalized Fermat equation, and see how studying its integral points leads one to study quotient stacks. We will then very quickly turn and run away from the general picture to a particularly simple example of these quotient stacks, the M-curves of Darmon-Granville, and how they can be used to say something about integral points without having to actually know what the hell a stack is.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019&diff=17671NTSGrad Spring 20192019-08-26T16:00:20Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_2| On <math>\ell</math>-torsion in class groups of number fields]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_9| Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_16| The march towards Malle's conjecture]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_23|Insufficiency of the Brauer Manin obstruction]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_30|The Cohen-Lenstra Heuristics]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| [[NTSGRAD_Spring_2019/Abstracts#May_7|Stacky Curves and the Generalized Fermat Equation]]<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17355NTSGrad Spring 2019/Abstracts2019-04-21T16:44:50Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD thesis. I will try my best to make this talk completely self-contained, i.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 2 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Weitong Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On <math>\ell</math>-torsion in class groups of number fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
According to Wei-Lun's request, I'll first introduce the big picture of the paper Nonvanishing of Hecke L-Functions and Bloch-Kato <math>p</math>-Selmer Groups, then focus on the quadratic case of the <math>\ell</math>-torsion in class groups.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 9 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sang Yup Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I’ll attempt to provide a number theorist’s explanation of flows and ergodicity, using one of our favorite spaces as an example. Then I’ll motivate the subject by presenting Sarnak’s conjecture on the randomness of the Mobius function and it’s corollaries.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Apr 16 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Niudun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The march towards Malle's Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will introduce Malle's conjecture and what is known about it. Then I will present an example using the most complicated group, <math>\mathbb{Z}/2\mathbb{Z}</math> to show how we count things in practice.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 23 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Insufficiency of the Brauer Manin obstruction''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will sketch an example of Poonen showing that the Brauer-Manin obstruction is insufficient in general to detect the non existence of rational points.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019&diff=17354NTSGrad Spring 20192019-04-21T16:43:37Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_2| On <math>\ell</math>-torsion in class groups of number fields]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_9| Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_16| The march towards Malle's conjecture]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_23|Insufficiency of the Brauer Manin obstruction]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17288NTSGrad Spring 2019/Abstracts2019-04-07T21:52:22Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD thesis. I will try my best to make this talk completely self-contained, i.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 2 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Weitong Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On <math>\ell</math>-torsion in class groups of number fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
According to Wei-Lun's request, I'll first introduce the big picture of the paper Nonvanishing of Hecke L-Functions and Bloch-Kato <math>p</math>-Selmer Groups, then focus on the quadratic case of the <math>\ell</math>-torsion in class groups.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 9 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sang Yup Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I’ll attempt to provide a number theorist’s explanation of flows and ergodicity, using one of our favorite spaces as an example. Then I’ll motivate the subject by presenting Sarnak’s conjecture on the randomness of the Mobius function and it’s corollaries.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019&diff=17287NTSGrad Spring 20192019-04-07T21:51:10Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_2| On <math>\ell</math>-torsion in class groups of number fields]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_9| Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17209NTSGrad Spring 2019/Abstracts2019-03-25T00:28:05Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over Q''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD theses. I will try my best to make this talk completely self-contained. I.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019&diff=17208NTSGrad Spring 20192019-03-25T00:26:32Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over Q]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16995Graduate Algebraic Geometry Seminar2019-02-19T16:23:04Z<p>Bboggess: /* March 13 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Name<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.<br />
|} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Dial M_1,1 for moduli<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
|} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16994Graduate Algebraic Geometry Seminar2019-02-19T16:21:08Z<p>Bboggess: /* Spring 2019 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Name<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.<br />
|} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16993Graduate Algebraic Geometry Seminar2019-02-19T16:20:54Z<p>Bboggess: /* Spring 2019 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli.]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Name<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.<br />
|} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Reading_Seminar_2018-19&diff=16925Reading Seminar 2018-192019-02-14T17:52:28Z<p>Bboggess: /* Talk Schedule */</p>
<hr />
<div>==Overview==<br />
My (Daniel's) experience has been that reading seminars have diminishing returns: they run out of steam after about 8 lectures on a certain book, as everyone starts falling behind, etc. I was thinking aim broader (rather than deeper), covering 3 books, but with fewer lectures. My idea is to partly cover: Beauville's "Complex Algebraic Surfaces"; Atiyah's "K-theory" (1989 edition); and Harris and Morrison's "Moduli of Curves". We would do about 6-8 lectures on each. This allows us to reboot every two months, which I hope will be mentally refreshing and will allow people who have lost the thread of the book to rejoin. Anyways, it's an experiment!<br />
<br />
Some notes:<br />
<ul><br />
<li>Here is lecture notes from Ravi Vakil on Complex Algebraic Surfaces "http://math.stanford.edu/~vakil/02-245/index.html"<br />
<li> Each book will have a co-organizer: Wanlin Li for Beauville's book; Michael Brown for Atiyah's book; and Rachel Davis for Harris and Mumford's book. Thanks!</li><br />
<li>I left some "Makeup" dates in the schedule with the idea that we would most likely take a week off on those dates. But if we need to miss another date (because of a conflict with a special colloquium or some other event), then we can use those as makeup slots.</li><br />
</ul><br />
<br />
We are experimenting with lots of new formats in this year's seminar. If you aren't happy with how the reading seminar is going, please let one of the organizers (Daniel, Wanlin, Michael, or Rachel) know and we will do our best to get things back on a helpful track.<br />
<br />
==Time and Location==<br />
Talks will be on Fridays from 11:00-11:45 in B329. This semester, Daniel is planning to keep a VERY HARD watch on the clock.<br />
<br />
== Talk Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | sections<br />
<br />
|-<br />
|September 7<br />
|Wanlin Li<br />
|Beauville I<br />
|-<br />
|September 14<br />
|Rachel Davis<br />
|Beauville II<br />
|-<br />
|September 21<br />
|Brandon Boggess<br />
|Beauville II and III<br />
|-<br />
|September 28<br />
|Mao Li<br />
|Beauville III<br />
|-<br />
|October 5<br />
|Wendy Cheng<br />
|Beauville IV<br />
|-<br />
|October 12<br />
|Soumya Sankar<br />
|Beauville V<br />
|-<br />
|October 19<br />
|David Wagner<br />
|Beauville V and VI<br />
|-<br />
|October 26<br />
|Dan Corey<br />
|Beauville VII and VIII<br />
|-<br />
|November 2<br />
|No Meeting<br />
|Break<br />
|-<br />
|November 9<br />
|Michael Brown<br />
|Atiyah 1 (Overview of goals of the seminar, Section 2.1) <br />
|-<br />
|November 16<br />
|Asvin Gothandaraman<br />
|Atiyah 2 (Section 2.2)<br />
|-<br />
|November 23<br />
|NO MEETING<br />
|Thanksgiving<br />
|-<br />
|November 30<br />
|NO MEETING<br />
|<br />
|-<br />
|SEMESETER BREAK<br />
|No meetings<br />
|<br />
|-<br />
|January 25<br />
|Daniel Erman<br />
|Atiyah 3 (Section 2.5: Examples)<br />
|-<br />
|February 1<br />
|Rachel Davis<br />
|Atiyah 4 (Section 2.3: Bott periodicity)<br />
|-<br />
|February 8<br />
|Michael Brown<br />
|Atiyah 5 (Thom isomorphism)<br />
|-<br />
|February 15<br />
|Mao Li<br />
|Algebraic K theory, Localization theorem and flag variety.<br />
|-<br />
|February 22<br />
|No Meeting<br />
|<br />
|-<br />
|March 1<br />
| Juliette Bruce<br />
|Moduli 1<br />
|-<br />
|March 8<br />
|Niudun Wang<br />
|Moduli 2<br />
|-<br />
|March 15<br />
|Rachel Davis<br />
|Moduli 3<br />
|-<br />
|March 22<br />
|NO MEETING<br />
|Spring recess<br />
|-<br />
|March 29<br />
|Michael Brown<br />
|Moduli 4<br />
|-<br />
|April 5<br />
|Brandon Boggess<br />
|Moduli 5<br />
|-<br />
|April 12<br />
|??<br />
|Moduli 6<br />
|-<br />
|April 19<br />
|??<br />
|Moduli 7<br />
|}<br />
<br />
==How to plan your talk==<br />
One key to giving good talks in a reading seminar is to know how to refocus the material that you read. Instead of going through the chapter lemma by lemma, you should ask: What is the main idea in this section? It could be a theorem, a definition, or even an example. But after reading the section, decide what the most important idea is and be sure to highlight early on.<br />
<br />
You will probably need to skip the proofs--and even the statements--of many of the lemmas and other results in the chapter. This is a good thing! The reason someone attends a talk, as opposed to just reading the material on their own, is because they want to see the material from the perspective of someone who has thought it about carefully.<br />
<br />
Also, make sure to give clear examples.<br />
<br />
<br />
==Feedback on talks==<br />
One of the goals for this semester is to help the speakers learn to give better talks. Here is our plan:<br />
<br />
<li> Feedback session: This is like a streamlined version of what creative writing workshops do. Every week, we reserve 15 minutes (12:35-12:50) for the entire audience to critique that week’s speaker. Comments will be friendly and constructive. A key rule is that the speaker is not allowed to speak until the last 5 minutes.</li><br />
<br />
<li> Partner: We assign a “partner” each week (usually the previous week's speaker). The partner will meet for 20-30 minutes with the speaker in advance to:<br />
<ol> Discuss a plan for the talk. Here the speaker can outline what they see as the main ideas, and the partner can share any wisdom gleaned from their experience the previous week. </ol><br />
<ol> Ask the speaker if there are any particular things that the speaker would like feedback on (e.g. pacing, boardwork, clarity of voice, etc.). </ol><br />
The partner would also take notes during the feedback session, to give the speaker a record of the conversation.<br />
</li><br />
<br />
This is very much an experiment, and while it might be intimidating at first, I actually think it could really help everyone (the speakers and the audience members too).</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019&diff=16892NTSGrad Spring 20192019-02-10T22:03:00Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | Soumya Sankar<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=16891NTSGrad Spring 2019/Abstracts2019-02-10T22:01:44Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16275Graduate Algebraic Geometry Seminar2018-10-25T14:24:23Z<p>Bboggess: /* October 31 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov/David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner/Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| TBD]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16274Graduate Algebraic Geometry Seminar2018-10-25T14:23:35Z<p>Bboggess: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov/David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner/Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| TBD]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://wiki.math.wisc.edu/index.php?title=Abelian_Varieties_2018&diff=15151Abelian Varieties 20182018-02-19T15:11:26Z<p>Bboggess: /* Talk Schedule */</p>
<hr />
<div>== Overview ==<br />
This reading seminar will cover Kempf's "Complex Abelian Varieties and Theta Functions" book. Talks will be Mondays, 4:00-4:50 in Room B139.<br />
<br />
We can try to cover Chapters 1-7 and Chapter 11 and maybe some topics from the other chapters of Birkenhake and Lange's "Complex Abelian Varieties" as time permits.<br />
<br />
== Talk Schedule ==<br />
The following schedule might be adjusted as we go, depending on whether it seems too fast or not.<br />
<br />
Here is the [[https://www.math.wisc.edu/wiki/images/TOC.pdf Table of Contents]] of Kempf's book.<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | sections<br />
<br />
|-<br />
|February 7<br />
|Rachel Davis<br />
|1.1-1.3<br />
|-<br />
|February 12<br />
|Soumya Sankar<br />
|1.4-1.5<br />
|-<br />
|February 19<br />
|Michael Brown<br />
|2.1-2.2<br />
|-<br />
|February 26<br />
|Solly Parenti<br />
|2.3-2.4<br />
|-<br />
|March 5<br />
|TBD<br />
|3.1-3.3<br />
|-<br />
|March 12<br />
|Moisés Herradón Cueto<br />
|3.4-3.6<br />
|-<br />
|March 19<br />
|Brandon Boggess<br />
|4<br />
|-<br />
|March 26<br />
|No meeting<br />
|Spring Break<br />
|-<br />
|April 2<br />
|Mao Li<br />
|5.1-5.3<br />
|-<br />
|April 9<br />
|TBD<br />
|5.3-5.5<br />
|-<br />
|April 16<br />
|TBD<br />
|6<br />
|-<br />
|April 23<br />
|TBD<br />
|7<br />
|-<br />
|April 30<br />
|TBD<br />
|11<br />
|-<br />
|May 7<br />
|TBD<br />
|???<br />
|-<br />
|}</div>Bboggess