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https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=13340
NTSGrad
2017-02-11T06:01:42Z
<p>Blalberts: /* Spring 2017 Semester */</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:''' Van Vleck B119<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2017 Semester =<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" | Jan 24<br />
| bgcolor="#F0B0B0" align="center" | Daniel Hast<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 31<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 7<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 14<br />
| bgcolor="#F0B0B0" align="center" | Vlad Matei<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 21<br />
| bgcolor="#F0B0B0" align="center" | David Wagner<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 28<br />
| bgcolor="#F0B0B0" align="center" | Wanlin Li<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 7<br />
| bgcolor="#F0B0B0" align="center" | Dongxi Ye<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 14<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| ''Arizona Winter School''<br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 21<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| ''Spring Break''<br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 28<br />
| bgcolor="#F0B0B0" align="center" | Brandon Boggess<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 4<br />
| bgcolor="#F0B0B0" align="center" | Soumya Sankar<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 11<br />
| bgcolor="#F0B0B0" align="center" | Brandon Alberts<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 18<br />
| bgcolor="#F0B0B0" align="center" | Solly Parenti<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 25<br />
| bgcolor="#F0B0B0" align="center" | Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 2<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=13142
NTSGrad
2017-01-26T20:44:39Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B119<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2017 Semester =<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" | Jan 24<br />
| bgcolor="#F0B0B0" align="center" | Daniel Hast<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 31<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 7<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 14<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 21<br />
| bgcolor="#F0B0B0" align="center" | David Wagner<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 28<br />
| bgcolor="#F0B0B0" align="center" | Wanlin Li<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 7<br />
| bgcolor="#F0B0B0" align="center" | Dongxi Ye<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 14<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| ''Arizona Winter School''<br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 21<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| ''Spring Break''<br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 28<br />
| bgcolor="#F0B0B0" align="center" | Brandon Boggess<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 4<br />
| bgcolor="#F0B0B0" align="center" | Soumya Sankar<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 11<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 18<br />
| bgcolor="#F0B0B0" align="center" | Solly Parenti<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 25<br />
| bgcolor="#F0B0B0" align="center" | Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 2<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=13141
NTSGrad
2017-01-26T20:37:42Z
<p>Blalberts: /* 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:''' Van Vleck B119<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_25 ''Complex Multiplication'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_1 ''Splitting Varieties for Cup Products'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_15 ''Apollonian Circle Packings'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_29 ''Introducation to p-adic Hodge Theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE" align="center" | [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_6 ''Supersingular Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_13 ''Chebotarev Density Theorem'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_20 ''A Primer on the Main Conjecture of Iwasawa Theory'']<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=13140
NTSGrad
2017-01-26T20:37:19Z
<p>Blalberts: /* Organizers */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_25 ''Complex Multiplication'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_1 ''Splitting Varieties for Cup Products'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_15 ''Apollonian Circle Packings'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_29 ''Introducation to p-adic Hodge Theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE" align="center" | [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_6 ''Supersingular Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_13 ''Chebotarev Density Theorem'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_20 ''A Primer on the Main Conjecture of Iwasawa Theory'']<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2016&diff=13139
NTSGrad Fall 2016
2017-01-26T20:36:17Z
<p>Blalberts: GNTS Fall 2016</p>
<hr />
<div>= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_25 ''Complex Multiplication'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_1 ''Splitting Varieties for Cup Products'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_15 ''Apollonian Circle Packings'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_29 ''Introducation to p-adic Hodge Theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE" align="center" | [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_6 ''Supersingular Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_13 ''Chebotarev Density Theorem'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_20 ''A Primer on the Main Conjecture of Iwasawa Theory'']<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12880
NTSGrad/Abstracts
2016-12-25T03:24:07Z
<p>Blalberts: /* Dec 20 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Happy Thanksgiving!''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to p-adic Hodge theory''<br />
|-<br />
| bgcolor="#BCD2EE" | This is a survey of the motivation and main concepts of p-adic <br />
Hodge theory. I will discuss criteria for good reduction of elliptic <br />
curves, classical (complex) Hodge theory, types of p-adic <br />
representations (Hodge-Tate, de Rham, semistable, crystalline), and <br />
comparison isomorphisms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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" | ''Supersingular Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | As its name suggests, supersingular elliptic curves are super special. And being special made them useful. A few weeks ago I gave a talk at GAGS about bounding gonality of modular curves. A result I used there without proof is a consequence of special properties of supersingular elliptic curves. And I'm going to explain that in this talk. I will define what supersingular elliptic curves are and hopefully convince you that they are cute.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chebotarev Density Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | I don't have anything particularly interesting, since I will just talk about the proof of the theorem.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''A Primer on the Main Conjecture of Iwasawa Theory''<br />
|-<br />
| bgcolor="#BCD2EE" | This talk will introduce a basic case of a theorem that establishes a surprising relationship between L-functions and class groups. This talk will attempt to convey the structure of the proof as well as two key ideas that boil down to a clever uses of p-adic analysis and of ramification in number fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12879
NTSGrad/Abstracts
2016-12-25T03:23:31Z
<p>Blalberts: /* Dec 13 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Happy Thanksgiving!''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to p-adic Hodge theory''<br />
|-<br />
| bgcolor="#BCD2EE" | This is a survey of the motivation and main concepts of p-adic <br />
Hodge theory. I will discuss criteria for good reduction of elliptic <br />
curves, classical (complex) Hodge theory, types of p-adic <br />
representations (Hodge-Tate, de Rham, semistable, crystalline), and <br />
comparison isomorphisms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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" | ''Supersingular Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | As its name suggests, supersingular elliptic curves are super special. And being special made them useful. A few weeks ago I gave a talk at GAGS about bounding gonality of modular curves. A result I used there without proof is a consequence of special properties of supersingular elliptic curves. And I'm going to explain that in this talk. I will define what supersingular elliptic curves are and hopefully convince you that they are cute.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chebotarev Density Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | I don't have anything particularly interesting, since I will just talk about the proof of the theorem.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12878
NTSGrad/Abstracts
2016-12-25T03:23:03Z
<p>Blalberts: /* Dec 6 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Happy Thanksgiving!''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to p-adic Hodge theory''<br />
|-<br />
| bgcolor="#BCD2EE" | This is a survey of the motivation and main concepts of p-adic <br />
Hodge theory. I will discuss criteria for good reduction of elliptic <br />
curves, classical (complex) Hodge theory, types of p-adic <br />
representations (Hodge-Tate, de Rham, semistable, crystalline), and <br />
comparison isomorphisms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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" | ''Supersingular Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | As its name suggests, supersingular elliptic curves are super special. And being special made them useful. A few weeks ago I gave a talk at GAGS about bounding gonality of modular curves. A result I used there without proof is a consequence of special properties of supersingular elliptic curves. And I'm going to explain that in this talk. I will define what supersingular elliptic curves are and hopefully convince you that they are cute.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12877
NTSGrad/Abstracts
2016-12-25T03:22:29Z
<p>Blalberts: /* Nov 29 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Happy Thanksgiving!''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to p-adic Hodge theory''<br />
|-<br />
| bgcolor="#BCD2EE" | This is a survey of the motivation and main concepts of p-adic <br />
Hodge theory. I will discuss criteria for good reduction of elliptic <br />
curves, classical (complex) Hodge theory, types of p-adic <br />
representations (Hodge-Tate, de Rham, semistable, crystalline), and <br />
comparison isomorphisms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12876
NTSGrad/Abstracts
2016-12-25T03:22:00Z
<p>Blalberts: /* Nov 22 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Happy Thanksgiving!''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12875
NTSGrad/Abstracts
2016-12-25T03:21:44Z
<p>Blalberts: /* Nov 8 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | '''none'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12874
NTSGrad/Abstracts
2016-12-25T03:21:29Z
<p>Blalberts: /* Nov 1 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12873
NTSGrad/Abstracts
2016-12-25T03:20:54Z
<p>Blalberts: /* Nov 15 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Apollonian circle packings''<br />
|-<br />
| bgcolor="#BCD2EE" | To form an Apollonian gasket, first nest two circles of integer curvature inside a third so that the three circles are mutually tangent and the points of tangency are distinct. By continuing to place tangent circles, one obtains an intricate packing in which all circles drawn have integer curvature. Using strong approximation and facts about thin groups (plus cool analytic tools), we give a partial answer the non-trivial question of which integers can occur as curvatures in a given gasket. Similar results continue to hold when we introduce a natural generalization of the gasket (to be discussed in greater depth on Thursday) in which geometric features of the packing correspond to arithmetic properties of a chosen imaginary quadratic field. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12872
NTSGrad/Abstracts
2016-12-25T03:20:31Z
<p>Blalberts: /* Nov 8 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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" | ''Splitting Varieties for Cup Products''<br />
|-<br />
| bgcolor="#BCD2EE" | I will define splitting varieties, and then show a method for constructing a large class of them. To convince you that this is not a tremendous waste of time, an automatic realization result for Galois groups will be given as an application of our splitting varieties.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12871
NTSGrad
2016-12-25T03:19:41Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_25 ''Complex Multiplication'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_1 ''Splitting Varieties for Cup Products'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_15 ''Apollonian Circle Packings'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | none<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_29 ''Introducation to p-adic Hodge Theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE" align="center" | [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_6 ''Supersingular Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_13 ''Chebotarev Density Theorem'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_20 ''A Primer on the Main Conjecture of Iwasawa Theory'']<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12607
NTSGrad
2016-10-24T20:17:17Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_25 ''Complex Multiplication'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12606
NTSGrad/Abstracts
2016-10-24T20:16:02Z
<p>Blalberts: /* Oct 25 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Complex Multiplication''<br />
|-<br />
| bgcolor="#BCD2EE" | As a youth, I had recurring nightmares about abelian extensions of number fields. Kronecker and Weber tell us about abelian extensions of Q, but even in the next simplest case, quadratic fields, what the Hecke can we say about these extensions? Deuring this talk, we will see what elliptic curves can tell us about extensions of imaginary quadratic fields. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12605
NTSGrad
2016-10-24T20:15:30Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_25 ''Complex Multiplication'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12599
NTSGrad
2016-10-24T05:29:29Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12508
NTSGrad/Abstracts
2016-10-17T06:28:09Z
<p>Blalberts: /* Oct 18 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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" | ''Cohen Lenstra Heuristics for p=2, or the lack thereof''<br />
|-<br />
| bgcolor="#BCD2EE" | I will introduce Cohen and Lenstra's Heuristics and talk about why they don't work for p=2. I will also talk about the alternative route to understanding the two-power torsion of the class group, in particular the work of Fouvry-Kluners and Gerth.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12507
NTSGrad/Abstracts
2016-10-17T06:27:34Z
<p>Blalberts: /* Oct 11 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular Forms and Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I will give a quick review of the basics for the classical case of Galois representations associated to modular forms, including the definition of modular forms, Hecke operators, elliptic curves, Galois representations arising from the Tate modules of elliptic curves, and the Modularity Theorem (i.e. the Taniyama-Shimura-Weil conjecture) that every elliptic curve defined over Q is modular.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12506
NTSGrad/Abstracts
2016-10-17T06:27:07Z
<p>Blalberts: /* Oct 4 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to arboreal Galois representations''<br />
|-<br />
| bgcolor="#BCD2EE" | Arboreal Galois representations are representations of Galois <br />
groups as automorphism groups of certain trees. We'll introduce the main <br />
definitions, see how iterating polynomial functions gives an abundant <br />
source of arboreal representations, and survey some of the major <br />
theorems and conjectures about these representations.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12505
NTSGrad/Abstracts
2016-10-17T06:26:35Z
<p>Blalberts: /* Sep 27 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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" | ''Modular forms of half integral weight''<br />
|-<br />
| bgcolor="#BCD2EE" | Usually when we think of modular forms we think of functions that gain an integral power of the automorphic factor under a group action. However we can generalize this notion to allow half integral weights. I will describe how this generalization works and it's connections to the theory of integral weight modular forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12504
NTSGrad
2016-10-17T06:25:52Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_27 ''Modular forms of half integral weight'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_4 ''Introduction to arboreal Galois representations'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_11 ''Modular Forms and Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_18 ''Cohen Lenstra Heuristics for p=2, or the lack thereof'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12481
NTSGrad
2016-10-11T08:48:39Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~pyu22/ Peng Yu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12362
NTSGrad/Abstracts
2016-09-20T04:25:20Z
<p>Blalberts: /* Sep 20 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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" | ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves''<br />
|-<br />
| bgcolor="#BCD2EE" | I'm going to talk about how Gauss's genus theory characterized 2 torsion elements of the class group for imaginary quadratic fields and how to use 2 decent to compute the 2-Selmer group for an elliptic curve.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12361
NTSGrad
2016-09-20T04:24:03Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_20 ''Gauss's Genus Theory and 2-Selmer Groups of Elliptic Curves'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~peiw7/ Peng Wei]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12279
NTSGrad/Abstracts
2016-09-12T20:02:01Z
<p>Blalberts: /* Sep 13 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded.<br />
<br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12278
NTSGrad/Abstracts
2016-09-12T20:01:19Z
<p>Blalberts: /* Sep 13 */</p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Overview of the Discrete Log Problem''<br />
|-<br />
| bgcolor="#BCD2EE" | The discrete logarithm problem (DLP) was first proposed as a hard problem in cryptography in the seminal article of Diffie and Hellman. Since then, together with factorization, it has become one of the two major pillars of public key cryptography.<br />
In its simplest version for $\mathbb{Z}/p\mathbb{Z}$, the problem is given $b\hspace{2mm} ( \text{mod}\hspace{2mm} p)$ and $b^n \hspace{2mm}(\text{mod} \hspace{2mm} p)$ to find $n$. <br />
As far as we know, this problem is VERY HARD to solve quickly. Nobody has admitted publicly to having proved that the discrete log can't be solved quickly, but many very smart people have tried hard and not succeeded. <br />
This is a prep talk for the Thursday seminar 9/15/2016<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12277
NTSGrad
2016-09-12T19:59:12Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_13 ''Overview for the Discrete Log Problem'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~peiw7/ Peng Wei]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12250
NTSGrad
2016-09-08T19:31:48Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~peiw7/ Peng Wei]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dwagner5/ David Wagner]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12192
NTSGrad
2016-09-04T22:37:30Z
<p>Blalberts: /* 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:''' Van Vleck B235<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12191
NTSGrad
2016-09-04T22:33:43Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12190
NTSGrad
2016-09-04T22:33:21Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/ABSTRACT#Sep_06 ''Introduction to the Cohen-Lenstra Measure'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12189
NTSGrad
2016-09-04T22:32:21Z
<p>Blalberts: /* Organizers */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| Introduction to the Cohen-Lenstra Measure<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12188
NTSGrad/Abstracts
2016-09-04T22:31:58Z
<p>Blalberts: </p>
<hr />
<div>== Sep 06 ==<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 Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to the Cohen-Lenstra Measure''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Cohen-Lenstra heuristics describe a conjectured probability distribution for the class group of quadratic fields. In this talk, I will give a brief introduction to the heuristic and how it is related to random groups. The remainder of the talk will focus on the Cohen-Lenstra probability measure for choosing a random p-group. This talk is based on a similar talk given by Bjorn Poonen.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 27 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 18 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 8 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 6 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 13 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 20 ==<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%" | ''''''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~grizzard/ Bobby Grizzard]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015&diff=12187
NTSGrad Fall 2015
2016-09-04T22:10:43Z
<p>Blalberts: /* Fall 2015 Semester */</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:''' Van Vleck B119<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Sep_15 ''The Important Questions'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~eramos/ Eric Ramos]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Sep_29 ''Generalized Representation Stability and FI_d-modules'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" |[http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Oct_20 ''Untitled'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Oct_27 ''How I accidentally became a topologist: a cautionary tale'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Nov_3 ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Nov_24 ''Introduction to Singular Moduli'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Dec_01 ''Number theory and modern cryptography'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Dec_08 ''Generating random factored numbers and ideals, easily'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2015/Abstracts#Dec_15 ''Introduction to linear code and algebraic geometry code'']<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad/Abstracts&diff=12186
NTSGrad/Abstracts
2016-09-04T22:09:40Z
<p>Blalberts: Blalberts moved page NTSGrad/Abstracts to NTSGrad Fall 2015/Abstracts: Old</p>
<hr />
<div>#REDIRECT [[NTSGrad Fall 2015/Abstracts]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=12185
NTSGrad Fall 2015/Abstracts
2016-09-04T22:09:40Z
<p>Blalberts: Blalberts moved page NTSGrad/Abstracts to NTSGrad Fall 2015/Abstracts: Old</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 08 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generating random factored numbers and ideals, easily''<br />
|-<br />
| bgcolor="#BCD2EE" | Say we want to generate a number, up to some bound N, uniformly at random, but we also want to know its factorization. We could generate a number and then factor it, but factoring isn't known to be polynomial time. In his dissertation, Eric Bach gave a polynomial time way to do this. We will present an alternative polynomial time algorithm for generating a number and its factorization uniformly at random. We will then extend this to the problem of generating ideals in number fields and their factorization uniformly at random, in polynomial time. If time permits, we will discuss how to extend this to arbitrary number fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to linear code and algebraic geometry code''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Linear code is an important kind of error correcting code. I will introduce some basic knowledge of linear code and then focus on those linear codes arising from algebraic curves. We will see how the study of algebraic curve over finite field sheds light on coding theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=12184
NTSGrad
2016-09-04T22:08:51Z
<p>Blalberts: /* Fall 2016 Semester */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2016 Semester =<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" | Sept 6<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| Introduction to the Cohen-Lenstra Measure<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sept 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~uwwanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE" align="center" | <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 20<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<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 />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=11935
NTSGrad
2016-06-18T19:40:31Z
<p>Blalberts: /* Spring 2016 Semester */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2016 Semester =<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" | DATE<br />
| bgcolor="#F0B0B0" align="center" | '''SPEAKER'''<br />
| bgcolor="#BCE2FE"| [ ''TITLE'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 26<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| Counting Categorically<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 2<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| Representation theory and random walks on finite groups<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 9<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| The Local-to-Global Principle and Approximation Theorems<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 16<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| Conductors and Minimal Discriminants of Elliptic Curves<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 23<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~steinberg/ Jason Steinberg]<br />
| bgcolor="#BCE2FE"| Borcherds product expansions<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| Heights on Projective Space<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 8<br />
| bgcolor="#F0B0B0" align="center" | Joseph Gunther<br />
| bgcolor="#BCE2FE"| moved to Thursday<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire]<br />
| bgcolor="#BCE2FE"| Stable and Unstable Homology of Configuration Spaces<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| Spring Break, no talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| ''Introduction to Honda-Tate Theory''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 5<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| Random Matrix theory and L-functions<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 12<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| On the p-torsion of abelian varieties over characteristic p<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 19<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| What's the point of curves of genus greater than 1?<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 26<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| ''Schoof's algorithm for counting points on elliptic curves''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| Introduction to additive combinatorics<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=11149
NTSGrad
2016-01-23T23:45:41Z
<p>Blalberts: /* Organizers */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2016 Semester =<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" | DATE<br />
| bgcolor="#F0B0B0" align="center" | '''SPEAKER'''<br />
| bgcolor="#BCE2FE"| [ ''TITLE'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 26<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 2<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 9<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 16<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 23<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~steinberg/ Jason Steinberg]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 8<br />
| bgcolor="#F0B0B0" align="center" | Joseph Gunther<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| Spring Break, no talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 5<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 12<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 19<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Brandon Alberts (blalberts@math.wisc.edu)<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts
https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=11148
NTSGrad
2016-01-23T23:36:10Z
<p>Blalberts: /* Spring 2016 Semester */</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:''' Van Vleck B129<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 should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2016 Semester =<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" | DATE<br />
| bgcolor="#F0B0B0" align="center" | '''SPEAKER'''<br />
| bgcolor="#BCE2FE"| [ ''TITLE'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 26<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 2<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~dalbye/ Ewan Dalby]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 9<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 16<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 23<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~steinberg/ Jason Steinberg]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 8<br />
| bgcolor="#F0B0B0" align="center" | Joseph Gunther<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| Spring Break, no talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 29<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jiuyawang/ Jiuya Wang]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 5<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 12<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 19<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>
Blalberts