https://hilbert.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Pirnes&feedformat=atomUW-Math Wiki - User contributions [en]2021-07-26T03:25:44ZUser contributionsMediaWiki 1.30.1https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=21037Graduate Algebraic Geometry Seminar2021-03-22T17:26:25Z<p>Pirnes: /* Spring 2021 */</p>
<hr />
<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM CST<br />
<br />
'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 18<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 18| An Introduction to the Deformation Theory of Complete Intersection Singularities]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Reconstruction conjecture in graph theory (Note: special time at noon!)]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to the Deformation Theory of Complete Intersection Singularities<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Essentially what it says in the title; I'll give a fairly laid-back overview of some of the basic definitions and results about deformations of complete intersection singularities, including the Kodaira-Spencer map and the existence of versal deformations in the isolated case. If time permits, I'll discuss Morsification of isolated singularities. Very little background will be assumed.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Let f_1,...,f_r in k[x_1,...,x_n] be homogeneous polynomial of degree d. Ananyan and Hochster (2016) proved that there exists a bound N=N(r,d) where if collective strength of f_1,...,f_r is greater than or equal to N, then f_1,...,f_r are regular sequence. In this paper, we study the explicit bound N(r,d) when $r=3$ and d=2,3 and show that N(3,2)=2 and N(3,3)>2.<br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory (Note: special time at noon!)<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The deck of a graph with n vertices is a multiset of n unlabeled graphs, each obtained from the original graph by deleting a vertex (and the edges incident to it). The reconstruction conjecture says that if two finite simple graphs with at least three vertices have the same deck, then they are isomorphic. The talk is going to focus on examples, and does not assume previous knowledge about graph theory.<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=21036Graduate Algebraic Geometry Seminar2021-03-22T17:24:47Z<p>Pirnes: /* April 1 */</p>
<hr />
<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM CST<br />
<br />
'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 18<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 18| An Introduction to the Deformation Theory of Complete Intersection Singularities]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Reconstruction conjecture in graph theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to the Deformation Theory of Complete Intersection Singularities<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Essentially what it says in the title; I'll give a fairly laid-back overview of some of the basic definitions and results about deformations of complete intersection singularities, including the Kodaira-Spencer map and the existence of versal deformations in the isolated case. If time permits, I'll discuss Morsification of isolated singularities. Very little background will be assumed.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Let f_1,...,f_r in k[x_1,...,x_n] be homogeneous polynomial of degree d. Ananyan and Hochster (2016) proved that there exists a bound N=N(r,d) where if collective strength of f_1,...,f_r is greater than or equal to N, then f_1,...,f_r are regular sequence. In this paper, we study the explicit bound N(r,d) when $r=3$ and d=2,3 and show that N(3,2)=2 and N(3,3)>2.<br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory (Note: special time at noon!)<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The deck of a graph with n vertices is a multiset of n unlabeled graphs, each obtained from the original graph by deleting a vertex (and the edges incident to it). The reconstruction conjecture says that if two finite simple graphs with at least three vertices have the same deck, then they are isomorphic. The talk is going to focus on examples, and does not assume previous knowledge about graph theory.<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=21025Graduate Algebraic Geometry Seminar2021-03-20T22:33:35Z<p>Pirnes: /* April 1 */</p>
<hr />
<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM CST<br />
<br />
'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 18<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 18| An Introduction to the Deformation Theory of Complete Intersection Singularities]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Reconstruction conjecture in graph theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to the Deformation Theory of Complete Intersection Singularities<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Essentially what it says in the title; I'll give a fairly laid-back overview of some of the basic definitions and results about deformations of complete intersection singularities, including the Kodaira-Spencer map and the existence of versal deformations in the isolated case. If time permits, I'll discuss Morsification of isolated singularities. Very little background will be assumed.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The deck of a graph with n vertices is a multiset of n unlabeled graphs, each obtained from the original graph by deleting a vertex (and the edges incident to it). The reconstruction conjecture says that if two finite simple graphs with at least three vertices have the same deck, then they are isomorphic. The talk is going to focus on examples, and does not assume previous knowledge about graph theory.<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=20843Graduate Algebraic Geometry Seminar2021-02-15T14:31:59Z<p>Pirnes: /* Spring 2021 */</p>
<hr />
<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM EST<br />
<br />
'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Alex Hoff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Reconstruction conjecture in graph theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=20842Graduate Algebraic Geometry Seminar2021-02-15T14:31:24Z<p>Pirnes: /* April 1 */</p>
<hr />
<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM EST<br />
<br />
'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Alex Hoff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=Dynamics_Seminar_2020-2021&diff=19738Dynamics Seminar 2020-20212020-09-10T22:36:39Z<p>Pirnes: </p>
<hr />
<div>The [[Dynamics Seminar]] meets virtually on '''Wednesdays''' from '''2:30pm - 3:20pm'''.<br />
<br> <br />
For more information, contact Chenxi Wu.<br />
To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 16<br />
|Andrew Zimmer (Wisconsin)<br />
|An introduction to Anosov representations I<br />
| (local)<br />
|-<br />
|September 23<br />
|Andrew Zimmer (Wisconsin)<br />
|An introduction to Anosov representations II<br />
| (local)<br />
|-<br />
|September 30<br />
|Chenxi Uw (Wisconsin)<br />
|TBA<br />
| (local)<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Andrew Zimmer===<br />
<br />
"An introduction to Anosov representations"<br />
<br />
Anosov representations are a special class of representations of finitely generated groups into Lie groups, which are defined using ideas from dynamics (namely, the theory of Anosov flows). In this talk, I will explain the definition (in a special case), give some examples, and describe some properties. I will focus on the case of representations into the general linear group where no background knowledge about Lie groups is required.<br />
<br />
<br />
===Chenxi Wu===<br />
<br />
"TBA"</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=18528Graduate Algebraic Geometry Seminar2019-12-06T00:28:05Z<p>Pirnes: /* December 11 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Fall 2019 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 18<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 18| M_g Potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 25<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 25| Derived Groups and Groupoids]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 9<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 9| Geometry of Generalized Fermat Curves ]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 16<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 16| Brauer groups and obstruction problems]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 23<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 23| The Ax-Grothendieck theorem and other fun stuff]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 30<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 30| Buildings and algebraic groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 6| Lorentzian Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 13<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 13| Tropicalization Blues]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 20| Computing Gr<span>&#246;</span>bner Bases of Submodules]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 27<br />
| bgcolor="#C6D46E"| Thanksgiving Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 27| ]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 4<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 4| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 11<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 11| Title TBD]]<br />
|}<br />
</center><br />
<br />
== September 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: M_g Potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In 1983, David Mumford proposed that the rational cohomology ring of Mg should be a polynomial algebra. I will discuss some of the history of Mumford's conjecture, possibly indicating a few ideas from the 2007 proof as the Madsen-Weiss theorem. If all goes well, the talk will take us through such diverse places as homotopy theory, representation stability, combinatorics of ribbon graph complexes, and deformations of algebras.<br />
<br />
|} <br />
</center><br />
<br />
== September 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Groups and Groupoids<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In this talk, we will discuss groups and groupoids in the derived category of dg schemes. I will focus on examples instead of the abstract theory. If X is a smooth subscheme of a smooth scheme S over the field of complex numbers, then the derived self-intersection of X in S is a groupoid. We will investigate the corresponding Lie algebroid of the groupoid I mentioned above, and exponential map between them.<br />
<br />
|} <br />
</center><br />
<br />
== October 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Geometry of Generalized Fermat Curves <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: We will look at the generalized Fermat equation, and see how studying its integral points leads one to study quotient stacks. We will then very quickly turn and run away from the general picture to a particularly simple example of these quotient stacks, the M-curves of Darmon-Granville, and how they can be used to say something about integral points without having to actually know what the hell a stack is.<br />
|} <br />
</center><br />
<br />
== October 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Brauer groups and obstruction problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Brauer groups are ubiquitous in arithmetic and algebraic geometry. I will try to describe different contexts in which they appear, ranging from Brauer groups of fields and class field theory, to obstructions to moduli problems and derived equivalences. <br />
|} <br />
</center><br />
<br />
== October 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Mine'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: The Ax-Grothendieck theorem and other fun stuff<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Ax-Grothendieck theorem says that any polynomial map from C^n to C^n that is injective is also surjective. The way this is proven is to note that the statement is trivial over finite fields, and somehow use this to work up to the complex numbers. We'll talk about this and other ways of translating information between finite fields and C.<br />
<br />
|} <br />
</center><br />
<br />
== October 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Buildings and algebraic groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will give a concrete introduction to the notion of a Tits building and its relationship to algebraic groups.<br />
<br />
|} <br />
</center><br />
<br />
== November 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lorentzian Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
Lorentzian polynomials are a family of multivariate polynomials recently introduced by Branden and Huh. We will define Lorentzian polynomials and survey some of their applications to combinatorics, representation theory, and computer science. The first 20 minutes of this talk should not require more than the ability to take partial derivatives of polynomials and basic linear algebra.<br />
|} <br />
</center><br />
<br />
== November 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropicalization Blues<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Tropicalization turns algebro-geometric objects into piecewise linear ones which can then be studied through the lens of combinatorics. In this talk, I will introduce the basic construction, then discuss some of the recent efforts to generalize and improve upon it, touching upon the Giansiracusa tropicalization and <s>developing</s> gazing wistfully in the direction of the machinery of ordered blueprints necessary for the Lorscheid tropicalization.<br />
<br />
|} <br />
</center><br />
<br />
== November 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Computing Gr<span>&#246;</span>bner Bases of Submodules<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In this talk, we will give motivation for and define Gr<span>&#246;</span>bner bases of submodules of finitely generated free modules over a polynomial ring S=k[x_1,...,x_r]. Not only are such bases extremely useful in constructive module theory and elimination theory, they are actually computable thanks to Buchberger's Algorithm. Further, they have a wide variety of applications in algebraic geometry including aiding in the computation of syzygies (kernels of maps of finitely generated, free S-modules), Hilbert functions, intersections of submodules, saturations, annihilators, projective closures, and elimination ideals. We will work through several examples and discuss some of these applications.<br />
<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Thanksgiving Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== December 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
|} <br />
</center><br />
<br />
== December 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Buchsbaum-Eisenbud-Horrocks conjecture<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Betti numbers are defined to be the ranks of the free modules in the free resolution of a module. The Buchsbaum-Eisenbud-Horrocks conjecture gives upper bounds for the Betti numbers. I'll state the conjecture and give some examples.<br />
<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=CCA_Reading_Group&diff=18212CCA Reading Group2019-10-18T15:07:07Z<p>Pirnes: /* Meeting Schedule */</p>
<hr />
<div>This is the page for the Fall 2019 Computational Commutative Algebra Reading Group, which is open to all UW Math grad students, but will require a certain amount of participation and work to receive credit.<br />
<br />
== Resources ==<br />
<br />
We plan to read Cox, Little, and O'Shea's ''Ideals, Varieties, and Algorithms'', which can be found here: [https://doc.lagout.org/science/0_Computer%20Science/2_Algorithms/Ideals%2C%20Varieties%2C%20and%20Algorithms%20%284th%20ed.%29%20%5BCox%2C%20Little%20%26%20O%27Shea%202015-06-14%5D.pdf].<br />
<br />
== Meeting Schedule ==<br />
<br />
10 weeks total, starting on Sept. 16, adjusting throughout the semester.<br />
<br />
Meetings will be on Mondays at 3:30-5:30pm, split into two sessions, in B129 VV.<br />
<br />
We will also have an additional problem session (optional) on Thursdays at 2:30-3:30pm in B119 VV.<br />
<br />
Exact schedule may vary slightly from week to week as needed.<br />
<br />
<br />
'''Approximate Reading Schedule:'''<br />
<br />
'''September 16'''<br />
<br />
a. Ch. 2: Grobner Bases, Sections 1-3 (Speaker: Caitlyn Booms)<br />
<br />
b. Ch. 2: Grobner Bases, Sections 4-6 (Speaker: Caitlyn Booms)<br />
<br />
<br />
'''September 23'''<br />
<br />
a. Ch. 2: Grobner Bases, Sections 7-8 (Speaker: Colin Crowley)<br />
<br />
b. Chapter 2 Exercises<br />
<br />
<br />
'''September 30'''<br />
<br />
a. Ch. 3: Elimination Theory, Sections 1-3 (Speaker: Caitlyn Booms)<br />
<br />
b. Ch. 3: Elimination Theory, Sections 4-6 (Speaker: Will Hardt)<br />
<br />
<br />
'''October 7'''<br />
<br />
a. Ch. 4: The Algebra-Geometry Dictionary, Sections 1-3 (Speaker: Erika Pirnes)<br />
<br />
b. Ch. 4: The Algebra-Geometry Dictionary, Sections 4-6 (Speaker: Alex Hof)<br />
<br />
<br />
'''October 14'''<br />
<br />
a. Ch. 4: The Algebra-Geometry Dictionary, Sections 7-9 (Speaker: Ivan Aidun)<br />
<br />
b. Chapter 3 and 4 Exercises (Led by Maya Banks)<br />
<br />
<br />
'''October 21'''<br />
<br />
a. Guest Lecture: Daniel Erman<br />
<br />
b. Catch up/Problem Session<br />
<br />
<br />
'''October 28'''<br />
<br />
a. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 1-3 (Speaker: Owen Goff)<br />
<br />
b. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 4-6 (Speaker: Erika Pirnes)<br />
<br />
<br />
'''November 4'''<br />
<br />
a. Ch. 8: Projective Algebraic Geometry, Sections 1-4 (Speaker: John Cobb)<br />
<br />
b. Ch. 8: Projective Algebraic Geometry, Sections 5-7 (Speaker: Eiki Norizuki)<br />
<br />
<br />
'''November 18'''<br />
<br />
a. Ch. 9: The Dimension of a Variety, Sections 1-3 (Speaker: Lorenzo Najt)<br />
<br />
b. Ch. 9: The Dimension of a Variety, Sections 4-6 (Speaker: Maya Banks)<br />
<br />
<br />
'''November 25'''<br />
<br />
a. Chapter 5, 8, and 9 Exercises<br />
<br />
b. Catch up/guest lecture<br />
<br />
== General Meeting Structure ==<br />
<br />
This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be an older grad student or professor. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be pretty flexible and will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We will also use Macaulay2 during the exercise sessions to get comfortable both computing examples by hand and by using a computer.<br />
<br />
'''If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu by Sept. 4, 2019.'''</div>Pirneshttps://hilbert.math.wisc.edu/wiki/index.php?title=CCA_Reading_Group&diff=17973CCA Reading Group2019-09-20T17:16:34Z<p>Pirnes: /* Meeting Schedule */</p>
<hr />
<div>This is the page for the Fall 2019 Computational Commutative Algebra Reading Group, which is open to all UW Math grad students, but will require a certain amount of participation and work to receive credit.<br />
<br />
== Resources ==<br />
<br />
We plan to read Cox, Little, and O'Shea's ''Ideals, Varieties, and Algorithms'', which can be found here: [https://doc.lagout.org/science/0_Computer%20Science/2_Algorithms/Ideals%2C%20Varieties%2C%20and%20Algorithms%20%284th%20ed.%29%20%5BCox%2C%20Little%20%26%20O%27Shea%202015-06-14%5D.pdf].<br />
<br />
== Meeting Schedule ==<br />
<br />
10 weeks total, starting on Sept. 16, adjusting throughout the semester.<br />
<br />
Meetings will be on Mondays at 3:30-5:30pm, split into two sessions, in B129 VV.<br />
<br />
We will also have additional problem sessions (optional) on Thursdays at 2:30-3:30pm in B119 VV, and on Fridays at 10-11am in B321 VV.<br />
<br />
Exact schedule may vary slightly from week to week as needed.<br />
<br />
<br />
'''Approximate Reading Schedule:'''<br />
<br />
'''September 16'''<br />
<br />
a. Ch. 2: Grobner Bases, Sections 1-3 (Speaker: Caitlyn Booms)<br />
<br />
b. Ch. 2: Grobner Bases, Sections 4-6 (Speaker: Caitlyn Booms)<br />
<br />
<br />
'''September 23'''<br />
<br />
a. Ch. 2: Grobner Bases, Sections 7-8 (Speaker: Maya Banks)<br />
<br />
b. Chapter 2 Exercises<br />
<br />
<br />
'''September 30'''<br />
<br />
a. Ch. 3: Elimination Theory, Sections 1-3 (Speaker: Colin Crowley)<br />
<br />
b. Ch. 3: Elimination Theory, Sections 4-6 (Speaker: Will Hardt)<br />
<br />
<br />
'''October 7'''<br />
<br />
a. Ch. 4: The Algebra-Geometry Dictionary, Sections 1-3 (Speaker: Erika Pirnes)<br />
<br />
b. Ch. 4: The Algebra-Geometry Dictionary, Sections 4-6 (Speaker: Alex Hof)<br />
<br />
<br />
'''October 14'''<br />
<br />
a. Ch. 4: The Algebra-Geometry Dictionary, Sections 7-9 (Speaker: Ivan Aidun)<br />
<br />
b. Chapter 3 and 4 Exercises<br />
<br />
<br />
'''October 21'''<br />
<br />
a. Catch up/guest lecture<br />
<br />
b. Catch up/guest lecture<br />
<br />
<br />
'''October 28'''<br />
<br />
a. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 1-3 (Speaker: Owen Goff)<br />
<br />
b. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 4-6 (Speaker: Brandon Legried)<br />
<br />
<br />
'''November 4'''<br />
<br />
a. Ch. 8: Projective Algebraic Geometry, Sections 1-4 (Speaker: John Cobb)<br />
<br />
b. Ch. 8: Projective Algebraic Geometry, Sections 5-7 (Speaker: Eiki Norizuki)<br />
<br />
<br />
'''November 18'''<br />
<br />
a. Ch. 9: The Dimension of a Variety, Sections 1-3 (Speaker: Lorenzo Najt)<br />
<br />
b. Ch. 9: The Dimension of a Variety, Sections 4-6 (Speaker: Maya Banks)<br />
<br />
<br />
'''November 25'''<br />
<br />
a. Chapter 5, 8, and 9 Exercises<br />
<br />
b. Catch up/guest lecture<br />
<br />
== General Meeting Structure ==<br />
<br />
This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be an older grad student or professor. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be pretty flexible and will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We will also use Macaulay2 during the exercise sessions to get comfortable both computing examples by hand and by using a computer.<br />
<br />
'''If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu by Sept. 4, 2019.'''</div>Pirnes