https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Sotirov&feedformat=atomUW-Math Wiki - User contributions [en]2021-01-27T05:34:49ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=18265Graduate Algebraic Geometry Seminar2019-10-28T05:47:21Z<p>Sotirov: </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| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 20| Title TBD]]<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: <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:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<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:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <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:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <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:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMGSTAWG&diff=16885AMGSTAWG2019-02-08T21:14:07Z<p>Sotirov: </p>
<hr />
<div>=About=<br />
This page documents an ongoing effort of the Working Group for establishing an Association of Mathematics Graduate Students and Teaching Assistants. <br />
==Mailing list==<br />
Math graduate students interesting in helping are welcome to join the group by subscribing to the [https://admin.lists.wisc.edu/index.php?p=11&l=amgstawg mailing list|], which will be the primary way of organizing future meetings.<br />
<br />
=Meetings Minutes=<br />
<br />
==Meeting #2: 2019-01-27, Sunday 4:00pm, notes by Vladimir Sotirov==<br />
Present: Michel Alexis, Benjamin Bruce, Soumya Sankar, Vladimir Sotirov, David Wagner, Jenny Yeon<br />
<br />
===Structure of the representative body===<br />
# regular (e.g. monthly) meetings to discuss issues that may have been brought up<br />
# attending department meetings, which is a responsibility that should cycle so that the burden is not too high<br />
# 7 or 5 representatives total: if 7 then 4 pre-disseratotrs and 3 dissertators, perhaps 1 dissertator beyond funding guarantee<br />
# ideally the representatives will offer a diversity of perspectives: from various years, domestic and international students, various genders, etc; codifying this into an actual requirement seems unreasonable<br />
<br />
===Communication between the representative body and the student body===<br />
# a scheduled event/meeting at either the beginning or end of the semester, coupled with a survey at the opposite end of the semester<br />
# emails highlighting information from department meetings that is important to graduate students, e.g. policy changes<br />
# graduate students should have the ability to raise isssues to the representatives as an intermediate step before raising issues to department chair or faculty<br />
## we need to have clear guidance on how such issues should be handled<br />
## a list of example issues and a list of appropriate resources need to be compiled and available<br />
## perhaps there should be a special secretary position among the representatives, or possibly even in addition to the representatives, responsible for maintaining information<br />
# graduate students that "fall though the cracks" tend not to communicate very well<br />
## Bobby Grizzard would perhaps be a good faculty link for such cases<br />
## the peer mentoring project is anothe resource<br />
# Kathie can mentiong us during orientation, perhaps distribute a poster with the representatives' faces!<br />
# there should be a web-site<br />
<br />
===Initiating the association===<br />
<br />
# mention us during donuts?<br />
# An email to everyone soliciting self-nominations, requires concise bullet points of exactly what the representative role entails<br />
# Timeline: have all the information necessary to craft the self-nomination solicitation email by March 3rd (Bulgarian independence day); solicit such unitl spring break, have the association ready after spring break for visitor's day<br />
<br />
===Tasks for next time===<br />
# minutes (Vlad)<br />
# set up collaborative docs (google or university), maybe a web-site, where we can compile the information we need (Jenny)<br />
# compile resources for dealing with various issues (David)<br />
# come up with example issues (MIchel, perhaps Soumya)<br />
# write down roles and responsibilities (Soumya, perhaps Michel)<br />
# make the wiki page more readable, so that people would sign up for the mailing list (Ben)<br />
# organize next meeting between 11th and 18th February (Ben)<br />
<br />
==Meeting #1: 2018-12-16, Sunday 12:30pm, notes by Vladimir Sotirov==<br />
Present: Michel Alexis, Benjamin Bruce, Vladimir Sotirov, Jenny Yeon<br />
<br />
===Goals of the association:===<br />
We first discussed what the goals of the association might be.<br />
# to facilitate communication between graduate students and faculty:<br />
## have a graduate student attend department meetings whose role is to relay relevant information back to the graduate students, e.g. via a newsletter, and to communicate positions of graduate students on issues that concern them;<br />
## Michel mentioned Tonghai and Andreas are open to the above role, but would hesitate in allowing graduate students to ''vote'' at department meetings;<br />
## provide structured time (e.g. monthly meeting, perhaps referendums via grad-chat) for graduate students to discuss issues that should be brought up to department meetings or to respond to policies being discussed at department meetings.<br />
# to facilitate communication and support between graduate students:<br />
## maintain awareness of various groups and activities organized by graduate students, especially concerning academic support and mentoring, as well as general stress management or mental health support.<br />
# to assist and to mediate between faculty and individual or groups of graduate students whenever specific issues arise.<br />
# to document and keep records graduate student life<br />
## maintain a history of past discussions between graduate students and faculty, eliminating the need for folklore that shifts as students graduate, and allowing graduate student a "big picture" view;<br />
## maintaining some kind of useful FAQ for graduate students beyond the Graduate Student and TA Handbooks that the department offers/will offer, e.g. various activities organized by grad students like DRP, peer mentoring, etc.<br />
<br />
===Roles within the association:===<br />
We briefly talked about the roles of people within the association's representative body.<br />
# Representatives of various groups of students, e.g.<br />
## representatives from each year<br />
## representative from each academic status: pre-qualifiying exam, post-qualifyting exam but not dissertator, dissertator<br />
## representatives for international students, women, other groups and minorities<br />
# Representatives to attend department meetings<br />
# Specialists in mental health resources and academic issues<br />
<br />
===Getting people involved:===<br />
We then discussed how to move forward with the establishing of the association, and specifically with getting people involved in the working group to make sure that what finally comes to be is as broadly useful as possible.<br />
<br />
# Canvas people to let them know this is happening after we have concrete proposals that they can think over and comment on.<br />
# Announce the working group somehow, e.g. via mailing list<br />
# Perhaps have a google doc or some other collaborative document to house the drafts of the above goals and roles.<br />
<br />
===Tasks:===<br />
Finally, we assigned each other tasks to perform:<br />
# Typing up the minutes (Vladimir)<br />
# Establishing a google doc or wiki (Vladimir)<br />
# Establishing a mailing list (Vladimir)<br />
# Contact other department stewards via TAA (Ben)<br />
# Send out a when2meet in early January to determine next meeting</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMGSTAWG&diff=16758AMGSTAWG2019-01-29T00:16:41Z<p>Sotirov: Meeting #2 minutes; typos</p>
<hr />
<div>=About=<br />
This page documents an ongoing effort of the Working Group for establishing an Association of Mathematics Graduate Students and Teaching Assistants. <br />
<br />
Math graduate students interesting in helping are welcome to join the group by subscribing to the [https://admin.lists.wisc.edu/index.php?p=11&l=amgstawg mailing list|], which will be the primary way of organizing future meetings.<br />
<br />
==Meeting #2: 2019-01-27, Sunday 4:00pm, notes by Vladimir Sotirov==<br />
Present: Michel Alexis, Benjamin Bruce, Soumya Sankar, Vladimir Sotirov, David Wagner, Jenny Yeon<br />
<br />
===Structure of the representative body===<br />
# regular (e.g. monthly) meetings to discuss issues that may have been brought up<br />
# attending department meetings, which is a responsibility that should cycle so that the burden is not too high<br />
# 7 or 5 representatives total: if 7 then 4 pre-disseratotrs and 3 dissertators, perhaps 1 dissertator beyond funding guarantee<br />
# ideally the representatives will offer a diversity of perspectives: from various years, domestic and international students, various genders, etc; codifying this into an actual requirement seems unreasonable<br />
<br />
===Communication between the representative body and the student body===<br />
# a scheduled event/meeting at either the beginning or end of the semester, coupled with a survey at the opposite end of the semester<br />
# emails highlighting information from department meetings that is important to graduate students, e.g. policy changes<br />
# graduate students should have the ability to raise isssues to the representatives as an intermediate step before raising issues to department chair or faculty<br />
## we need to have clear guidance on how such issues should be handled<br />
## a list of example issues and a list of appropriate resources need to be compiled and available<br />
## perhaps there should be a special secretary position among the representatives, or possibly even in addition to the representatives, responsible for maintaining information<br />
# graduate students that "fall though the cracks" tend not to communicate very well<br />
## Bobby Grizzard would perhaps be a good faculty link for such cases<br />
## the peer mentoring project is anothe resource<br />
# Kathie can mentiong us during orientation, perhaps distribute a poster with the representatives' faces!<br />
# there should be a web-site<br />
<br />
===Initiating the association===<br />
<br />
# mention us during donuts?<br />
# An email to everyone soliciting self-nominations, requires concise bullet points of exactly what the representative role entails<br />
# Timeline: have all the information necessary to craft the self-nomination solicitation email by March 3rd (Bulgarian independence day); solicit such unitl spring break, have the association ready after spring break for visitor's day<br />
<br />
===Tasks for next time===<br />
# minutes (Vlad)<br />
# set up collaborative docs (google or university), maybe a web-site, where we can compile the information we need (Jenny)<br />
# compile resources for dealing with various issues (David)<br />
# come up with example issues (MIchel, perhaps Soumya)<br />
# write down roles and responsibilities (Soumya, perhaps Michel)<br />
# make the wiki page more readable, so that people would sign up for the mailing list (Ben)<br />
# organize next meeting between 11th and 18th February (Ben)=Meetings Minutes=<br />
==Meeting #1: 2018-12-16, Sunday 12:30pm, notes by Vladimir Sotirov==<br />
Present: Michel Alexis, Benjamin Bruce, Vladimir Sotirov, Jenny Yeon<br />
<br />
===Goals of the association:===<br />
We first discussed what the goals of the association might be.<br />
# to facilitate communication between graduate students and faculty:<br />
## have a graduate student attend department meetings whose role is to relay relevant information back to the graduate students, e.g. via a newsletter, and to communicate positions of graduate students on issues that concern them;<br />
## Michel mentioned Tonghai and Andreas are open to the above role, but would hesitate in allowing graduate students to ''vote'' at department meetings;<br />
## provide structured time (e.g. monthly meeting, perhaps referendums via grad-chat) for graduate students to discuss issues that should be brought up to department meetings or to respond to policies being discussed at department meetings.<br />
# to facilitate communication and support between graduate students:<br />
## maintain awareness of various groups and activities organized by graduate students, especially concerning academic support and mentoring, as well as general stress management or mental health support.<br />
# to assist and to mediate between faculty and individual or groups of graduate students whenever specific issues arise.<br />
# to document and keep records graduate student life<br />
## maintain a history of past discussions between graduate students and faculty, eliminating the need for folklore that shifts as students graduate, and allowing graduate student a "big picture" view;<br />
## maintaining some kind of useful FAQ for graduate students beyond the Graduate Student and TA Handbooks that the department offers/will offer, e.g. various activities organized by grad students like DRP, peer mentoring, etc.<br />
<br />
===Roles within the association:===<br />
We briefly talked about the roles of people within the association's representative body.<br />
# Representatives of various groups of students, e.g.<br />
## representatives from each year<br />
## representative from each academic status: pre-qualifiying exam, post-qualifyting exam but not dissertator, dissertator<br />
## representatives for international students, women, other groups and minorities<br />
# Representatives to attend department meetings<br />
# Specialists in mental health resources and academic issues<br />
<br />
===Getting people involved:===<br />
We then discussed how to move forward with the establishing of the association, and specifically with getting people involved in the working group to make sure that what finally comes to be is as broadly useful as possible.<br />
<br />
# Canvas people to let them know this is happening after we have concrete proposals that they can think over and comment on.<br />
# Announce the working group somehow, e.g. via mailing list<br />
# Perhaps have a google doc or some other collaborative document to house the drafts of the above goals and roles.<br />
<br />
===Tasks:===<br />
Finally, we assigned each other tasks to perform:<br />
# Typing up the minutes (Vladimir)<br />
# Establishing a google doc or wiki (Vladimir)<br />
# Establishing a mailing list (Vladimir)<br />
# Contact other department stewards via TAA (Ben)<br />
# Send out a when2meet in early January to determine next meeting</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMGSTAWG&diff=16685AMGSTAWG2019-01-23T01:18:31Z<p>Sotirov: </p>
<hr />
<div>=About=<br />
This page documents an ongoing effort of the Working Group for establishing an Association of Mathematics Graduate Students and Teaching Assistants. <br />
<br />
Math graduate students interesting in helping are welcome to join the group by subscribing to the [https://admin.lists.wisc.edu/index.php?p=11&l=amgstawg mailing list|], which will be the primary way of organizing future meetings.<br />
<br />
=Meeting #2=<br />
[https://www.when2meet.com/?7458418-J6fDy when2meet]<br />
<br />
=Meetings Minutes=<br />
==Meeting #1: 2018-12-16, Sunday 12:30pm, notes by Vladimir Sotirov==<br />
Present: Michel Alexis, Benjamin Bruce, Vladimir Sotirov, Jenny Yeon<br />
<br />
===Goals of the association:===<br />
We first discussed what the goals of the association might be.<br />
# to facilitate communication between graduate students and faculty:<br />
## have a graduate student attend department meetings whose role is to relay relevant information back to the graduate students, e.g. via a newsletter, and to communicate positions of graduate students on issues that concern them;<br />
## Michel mentioned Tonghai and Andreas are open to the above role, but would hesitate in allowing graduate students to ''vote'' at department meetings;<br />
## provide structured time (e.g. monthly meeting, perhaps referendums via grad-chat) for graduate students to discuss issues that should be brought up to department meetings or to respond to policies being discussed at department meetings.<br />
# to facilitate communication and support between graduate students:<br />
##) maintain awareness of various groups and activities organized by graduate students, especially concerning academic support and mentoring, as well as general stress management or mental health support.<br />
# to assist and to mediate between faculty and individual or groups of graduate students whenever specific issues arise.<br />
# to document and keep records graduate student life<br />
## maintain a history of past discussions between graduate students and faculty, eliminating the need for folklore that shifts as students graduate, and allowing graduate student a "big picture" view;<br />
## maintaining some kind of useful FAQ for graduate students beyond the Graduate Student and TA Handbooks that the department offers/will offer, e.g. various activities organized by grad students like DRP, peer mentoring, etc.<br />
<br />
===Roles within the association:===<br />
We briefly talked about the roles of people within the association's representative body.<br />
# Representatives of various groups of students, e.g.<br />
## representatives from each year<br />
## representative from each academic status: pre-qualifiying exam, post-qualifyting exam but not dissertator, dissertator<br />
## representatives for international students, women, other groups and minorities<br />
# Representatives to attend department meetings<br />
# Specialists in mental health resources and academic issues<br />
<br />
===Getting people involved:===<br />
We then discussed how to move forward with the establishing of the association, and specifically with getting people involved in the working group to make sure that what finally comes to be is as broadly useful as possible.<br />
<br />
# Canvas people to let them know this is happening after we have concrete proposals that they can think over and comment on.<br />
# Announce the working group somehow, e.g. via mailing list<br />
# Perhaps have a google doc or some other collaborative document to house the drafts of the above goals and roles.<br />
<br />
===Tasks:===<br />
Finally, we assigned each other tasks to perform:<br />
# Typing up the minutes (Vladimir)<br />
# Establishing a google doc or wiki (Vladimir)<br />
# Establishing a mailing list (Vladimir)<br />
# Contact other department stewards via TAA (Ben)<br />
# Send out a when2meet in early January to determine next meeting</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16684Algebra and Algebraic Geometry Seminar Spring 20192019-01-23T01:11:38Z<p>Sotirov: Undo revision 16682 by Sotirov (talk)</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Fall 2018 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Fall 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Spring 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 25<br />
|[http://www.math.utah.edu/~smolkin/ Daniel Smolkin (Utah)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|February 1<br />
|Juliette Bruce<br />
|Asymptotic Syzgies for Products of Projective Spaces<br />
|Local<br />
|-<br />
|February 8<br />
|[http://www.mit.edu/~ivogt/ Isabel Vogt (MIT)]<br />
| Low degree points on curves<br />
|Wanlin and Juliette<br />
|-<br />
|February 15<br />
|Pavlo Pylyavskyy (U. Minn)<br />
|TBD<br />
|Paul Terwilliger<br />
|-<br />
|February 22<br />
|Michael Brown<br />
|Chern-Weil theory for matrix factorizations<br />
|Local<br />
|-<br />
|March 1<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 19<br />
|[http://www-personal.umich.edu/~grifo/ Elo&iacute;sa Grifo (Michigan)]<br />
|TBD<br />
|TBD<br />
|-<br />
|April 26<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|May 3<br />
|TBD<br />
|TBD<br />
|TBD<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Juliette Bruce===<br />
<br />
'''Title: Asymptotic Syzygies for Products of Projective Spaces'''<br />
<br />
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.<br />
<br />
===Isabel Vogt===<br />
<br />
'''Title: Low degree points on curves'''<br />
<br />
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=16683Algebra and Algebraic Geometry Seminar Fall 20182019-01-23T01:09:37Z<p>Sotirov: Undo revision 16681 by Sotirov (talk)</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]], [[Algebra and Algebraic Geometry Seminar Spring 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings<br />
|Local<br />
|-<br />
|September 14<br />
|Akhil Mathew (U Chicago)<br />
|Kaledin's noncommutative degeneration theorem and topological Hochschild homology<br />
|Andrei<br />
|-<br />
|September 21<br />
|Andrei Caldararu<br />
|Categorical Gromov-Witten invariants beyond genus 1<br />
|Local<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|Conjecture D for matrix factorizations<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|Modified quantum difference Toda systems<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|[https://juliettebruce.github.io Juliette Bruce]<br />
|Covering Abelian Varieties and Effective Bertini<br />
|Local<br />
|-<br />
|November 2<br />
|[http://sites.nd.edu/b-taji/ Behrouz Taji] (Notre Dame)<br />
|Remarks on the Kodaira dimension of base spaces of families of manifolds<br />
|Botong Wang<br />
|-<br />
|November 9<br />
|[http://www-personal.umich.edu/~rohitna/ Rohit Nagpal (Michigan)]<br />
|Finiteness properties of the Steinberg representation.<br />
|John WG<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|December 7<br />
|<br />
|<br />
|<br />
|-<br />
|December 14<br />
|TBD (this date is now open again!)<br />
|TBD<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Akhil Mathew===<br />
<br />
'''Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology'''<br />
<br />
For a smooth proper variety over a field of characteristic<br />
zero, the Hodge-to-de Rham spectral sequence (relating the cohomology<br />
of differential forms to de Rham cohomology) is well-known to<br />
degenerate, via Hodge theory. A "noncommutative" version of this<br />
theorem has been proved by Kaledin for smooth proper dg categories<br />
over a field of characteristic zero, based on the technique of<br />
reduction mod p. I will describe a short proof of this theorem using<br />
the theory of topological Hochschild homology, which provides a<br />
canonical one-parameter deformation of Hochschild homology in<br />
characteristic p.<br />
<br />
===Andrei Caldararu===<br />
'''Categorical Gromov-Witten invariants beyond genus 1'''<br />
<br />
In a seminal work from 2005 Kevin Costello defined numerical invariants associated to a <br />
Calabi-Yau A-infinity category. These invariants are supposed to generalize the classical<br />
Gromov-Witten invariants (counting curves in a target symplectic manifold) when the category<br />
is taken to be the Fukaya category. In my talk I shall describe some of the ideas involved in Costello's<br />
approach and recent progress (with Junwu Tu) on extending computations of these invariants<br />
past genus 1.<br />
<br />
===Mark Walker===<br />
'''Conjecture D for matrix factorizations'''<br />
<br />
Matrix factorizations form a dg category whose associated homotopy category is equivalent to the stable category of maximum Cohen-Macaulay modules over a hypersurface ring. In the isolated singularity case, the dg category of matrix factorizations is "smooth" and "proper" --- non-commutative analogues of the same-named properties of algebraic varieties. In general, for any smooth and proper dg category, there exist non-commutative analogues of Grothendieck's Standard Conjectures for cycles on smooth and projective varieties. In particular, the non-commutative version of Standard Conjecture D predicts that numerical equivalence and homological equivalence coincide for such a dg category. Recently, Michael Brown and I have proven the non-commutative analogue of Conjecture D for the category of matrix factorizations of an isolated singularity over a field of characteristic 0. In this talk, I will describe our theorem in more detail and give a sense of its proof.<br />
<br />
===Oleksandr Tsymbaliuk===<br />
'''Modified quantum difference Toda systems'''<br />
<br />
The q-version of a Toda system associated with any Lie algebra was introduced independently by Etingof and Sevostyanov in 1999. In this talk, we shall discuss the generalization of this construction which naturally produces a family of 3^{rk(g)-1} similar integrable systems. One of the key ingredients in the proof is played by the fermionic formula for the J-factors (defined as pairing of two Whittaker vectors in Verma modules), due to Feigin-Feigin-Jimbo-Miwa-Mukhin. In types A and C, our construction admits an alternative presentation via local Lax matrices, similar to the classical construction of Faddeev-Takhtajan for the classical type A Toda system. Finally, we shall discuss the geometric interpretation of Whittaker vectors in type A. <br />
<br />
This talk is based on the joint work with M. Finkelberg and R. Gonin.<br />
<br />
===Juliette Bruce===<br />
'''Covering Abelian Varieties and Effective Bertini'''<br />
<br />
I will discuss recent work showing that every abelian variety is covered by a Jacobian whose dimension is bounded. This is joint with Wanlin Li.<br />
<br />
===Behrouz Taji===<br />
<br />
'''Remarks on the Kodaira dimension of base spaces of families of manifolds'''<br />
<br />
A conjecture of Shafarevich and Viehweg predicted that <br />
a family of smooth projective manifolds with good minimal models<br />
have (log-)general type base spaces, if the family has maximal variation.<br />
Generalizing this problem, Kebekus and Kovács conjectured that the <br />
Kodaira dimension of base spaces of such manifolds should <br />
define an upper bound for the variation in the family, even if the variation <br />
is not maximal. My aim in this talk is to discuss a strategy to solve this problem.<br />
<br />
===Rohit Nagpal===<br />
'''Finiteness properties of the Steinberg representation'''<br />
<br />
We will show that the Steinberg modules for the general linear groups form a Koszul monoid in an appropriate symmetric monoidal category. Using this we will find bounds on the codimension-one cohomology of level-3 congruence subgroups. This Koszulness result can also be used to show Ash--Putman--Sam homological vanishing theorem for the Steinberg representations. This is a joint work with Jeremy Miller and Peter Patzt.<br />
<br />
===John Wiltshire-Gordon===<br />
'''Computing with FI-modules'''<br />
<br />
We explain what an FI-module is, giving examples in algebra and combinatorics, and show how to compute with an FI-module. We then demonstrate a new result about FI-modules that is joint work with Peter Patzt.</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16682Algebra and Algebraic Geometry Seminar Spring 20192019-01-23T01:07:46Z<p>Sotirov: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Fall 2018 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar | this semester]] and for [[Algebra and Algebraic Geometry Seminar Fall 2019 | the next semester]]<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Spring 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 25<br />
|[http://www.math.utah.edu/~smolkin/ Daniel Smolkin (Utah)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|February 1<br />
|Juliette Bruce<br />
|Asymptotic Syzgies for Products of Projective Spaces<br />
|Local<br />
|-<br />
|February 8<br />
|[http://www.mit.edu/~ivogt/ Isabel Vogt (MIT)]<br />
| Low degree points on curves<br />
|Wanlin and Juliette<br />
|-<br />
|February 15<br />
|Pavlo Pylyavskyy (U. Minn)<br />
|TBD<br />
|Paul Terwilliger<br />
|-<br />
|February 22<br />
|Michael Brown<br />
|Chern-Weil theory for matrix factorizations<br />
|Local<br />
|-<br />
|March 1<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 19<br />
|[http://www-personal.umich.edu/~grifo/ Elo&iacute;sa Grifo (Michigan)]<br />
|TBD<br />
|TBD<br />
|-<br />
|April 26<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|May 3<br />
|TBD<br />
|TBD<br />
|TBD<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Juliette Bruce===<br />
<br />
'''Title: Asymptotic Syzygies for Products of Projective Spaces'''<br />
<br />
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.<br />
<br />
===Isabel Vogt===<br />
<br />
'''Title: Low degree points on curves'''<br />
<br />
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=16681Algebra and Algebraic Geometry Seminar Fall 20182019-01-23T01:07:10Z<p>Sotirov: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]], and for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the next semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings<br />
|Local<br />
|-<br />
|September 14<br />
|Akhil Mathew (U Chicago)<br />
|Kaledin's noncommutative degeneration theorem and topological Hochschild homology<br />
|Andrei<br />
|-<br />
|September 21<br />
|Andrei Caldararu<br />
|Categorical Gromov-Witten invariants beyond genus 1<br />
|Local<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|Conjecture D for matrix factorizations<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|Modified quantum difference Toda systems<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|[https://juliettebruce.github.io Juliette Bruce]<br />
|Covering Abelian Varieties and Effective Bertini<br />
|Local<br />
|-<br />
|November 2<br />
|[http://sites.nd.edu/b-taji/ Behrouz Taji] (Notre Dame)<br />
|Remarks on the Kodaira dimension of base spaces of families of manifolds<br />
|Botong Wang<br />
|-<br />
|November 9<br />
|[http://www-personal.umich.edu/~rohitna/ Rohit Nagpal (Michigan)]<br />
|Finiteness properties of the Steinberg representation.<br />
|John WG<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|December 7<br />
|<br />
|<br />
|<br />
|-<br />
|December 14<br />
|TBD (this date is now open again!)<br />
|TBD<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Akhil Mathew===<br />
<br />
'''Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology'''<br />
<br />
For a smooth proper variety over a field of characteristic<br />
zero, the Hodge-to-de Rham spectral sequence (relating the cohomology<br />
of differential forms to de Rham cohomology) is well-known to<br />
degenerate, via Hodge theory. A "noncommutative" version of this<br />
theorem has been proved by Kaledin for smooth proper dg categories<br />
over a field of characteristic zero, based on the technique of<br />
reduction mod p. I will describe a short proof of this theorem using<br />
the theory of topological Hochschild homology, which provides a<br />
canonical one-parameter deformation of Hochschild homology in<br />
characteristic p.<br />
<br />
===Andrei Caldararu===<br />
'''Categorical Gromov-Witten invariants beyond genus 1'''<br />
<br />
In a seminal work from 2005 Kevin Costello defined numerical invariants associated to a <br />
Calabi-Yau A-infinity category. These invariants are supposed to generalize the classical<br />
Gromov-Witten invariants (counting curves in a target symplectic manifold) when the category<br />
is taken to be the Fukaya category. In my talk I shall describe some of the ideas involved in Costello's<br />
approach and recent progress (with Junwu Tu) on extending computations of these invariants<br />
past genus 1.<br />
<br />
===Mark Walker===<br />
'''Conjecture D for matrix factorizations'''<br />
<br />
Matrix factorizations form a dg category whose associated homotopy category is equivalent to the stable category of maximum Cohen-Macaulay modules over a hypersurface ring. In the isolated singularity case, the dg category of matrix factorizations is "smooth" and "proper" --- non-commutative analogues of the same-named properties of algebraic varieties. In general, for any smooth and proper dg category, there exist non-commutative analogues of Grothendieck's Standard Conjectures for cycles on smooth and projective varieties. In particular, the non-commutative version of Standard Conjecture D predicts that numerical equivalence and homological equivalence coincide for such a dg category. Recently, Michael Brown and I have proven the non-commutative analogue of Conjecture D for the category of matrix factorizations of an isolated singularity over a field of characteristic 0. In this talk, I will describe our theorem in more detail and give a sense of its proof.<br />
<br />
===Oleksandr Tsymbaliuk===<br />
'''Modified quantum difference Toda systems'''<br />
<br />
The q-version of a Toda system associated with any Lie algebra was introduced independently by Etingof and Sevostyanov in 1999. In this talk, we shall discuss the generalization of this construction which naturally produces a family of 3^{rk(g)-1} similar integrable systems. One of the key ingredients in the proof is played by the fermionic formula for the J-factors (defined as pairing of two Whittaker vectors in Verma modules), due to Feigin-Feigin-Jimbo-Miwa-Mukhin. In types A and C, our construction admits an alternative presentation via local Lax matrices, similar to the classical construction of Faddeev-Takhtajan for the classical type A Toda system. Finally, we shall discuss the geometric interpretation of Whittaker vectors in type A. <br />
<br />
This talk is based on the joint work with M. Finkelberg and R. Gonin.<br />
<br />
===Juliette Bruce===<br />
'''Covering Abelian Varieties and Effective Bertini'''<br />
<br />
I will discuss recent work showing that every abelian variety is covered by a Jacobian whose dimension is bounded. This is joint with Wanlin Li.<br />
<br />
===Behrouz Taji===<br />
<br />
'''Remarks on the Kodaira dimension of base spaces of families of manifolds'''<br />
<br />
A conjecture of Shafarevich and Viehweg predicted that <br />
a family of smooth projective manifolds with good minimal models<br />
have (log-)general type base spaces, if the family has maximal variation.<br />
Generalizing this problem, Kebekus and Kovács conjectured that the <br />
Kodaira dimension of base spaces of such manifolds should <br />
define an upper bound for the variation in the family, even if the variation <br />
is not maximal. My aim in this talk is to discuss a strategy to solve this problem.<br />
<br />
===Rohit Nagpal===<br />
'''Finiteness properties of the Steinberg representation'''<br />
<br />
We will show that the Steinberg modules for the general linear groups form a Koszul monoid in an appropriate symmetric monoidal category. Using this we will find bounds on the codimension-one cohomology of level-3 congruence subgroups. This Koszulness result can also be used to show Ash--Putman--Sam homological vanishing theorem for the Steinberg representations. This is a joint work with Jeremy Miller and Peter Patzt.<br />
<br />
===John Wiltshire-Gordon===<br />
'''Computing with FI-modules'''<br />
<br />
We explain what an FI-module is, giving examples in algebra and combinatorics, and show how to compute with an FI-module. We then demonstrate a new result about FI-modules that is joint work with Peter Patzt.</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&diff=16680Algebra and Algebraic Geometry Seminar2019-01-23T01:06:09Z<p>Sotirov: Redirected page to Algebra and Algebraic Geometry Seminar Spring 2019</p>
<hr />
<div>#REDIRECT [[Algebra and Algebraic Geometry Seminar Spring 2019]]</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMGSTAWG&diff=16586AMGSTAWG2019-01-02T03:53:49Z<p>Sotirov: Document first meeting</p>
<hr />
<div>=About=<br />
This page documents an ongoing effort of the Working Group for establishing an Association of Mathematics Graduate Students and Teaching Assistants. <br />
<br />
Math graduate students interesting in helping are welcome to join the group by subscribing to the [https://admin.lists.wisc.edu/index.php?p=11&l=amgstawg mailing list|], which will be the primary way of organizing future meetings.<br />
=Meetings Minutes=<br />
==Meeting #1: 2018-12-16, Sunday 12:30pm, notes by Vladimir Sotirov==<br />
Present: Michel Alexis, Benjamin Bruce, Vladimir Sotirov, Jenny Yeon<br />
<br />
===Goals of the association:===<br />
We first discussed what the goals of the association might be.<br />
# to facilitate communication between graduate students and faculty:<br />
## have a graduate student attend department meetings whose role is to relay relevant information back to the graduate students, e.g. via a newsletter, and to communicate positions of graduate students on issues that concern them;<br />
## Michel mentioned Tonghai and Andreas are open to the above role, but would hesitate in allowing graduate students to ''vote'' at department meetings;<br />
## provide structured time (e.g. monthly meeting, perhaps referendums via grad-chat) for graduate students to discuss issues that should be brought up to department meetings or to respond to policies being discussed at department meetings.<br />
# to facilitate communication and support between graduate students:<br />
##) maintain awareness of various groups and activities organized by graduate students, especially concerning academic support and mentoring, as well as general stress management or mental health support.<br />
# to assist and to mediate between faculty and individual or groups of graduate students whenever specific issues arise.<br />
# to document and keep records graduate student life<br />
## maintain a history of past discussions between graduate students and faculty, eliminating the need for folklore that shifts as students graduate, and allowing graduate student a "big picture" view;<br />
## maintaining some kind of useful FAQ for graduate students beyond the Graduate Student and TA Handbooks that the department offers/will offer, e.g. various activities organized by grad students like DRP, peer mentoring, etc.<br />
<br />
===Roles within the association:===<br />
We briefly talked about the roles of people within the association's representative body.<br />
# Representatives of various groups of students, e.g.<br />
## representatives from each year<br />
## representative from each academic status: pre-qualifiying exam, post-qualifyting exam but not dissertator, dissertator<br />
## representatives for international students, women, other groups and minorities<br />
# Representatives to attend department meetings<br />
# Specialists in mental health resources and academic issues<br />
<br />
===Getting people involved:===<br />
We then discussed how to move forward with the establishing of the association, and specifically with getting people involved in the working group to make sure that what finally comes to be is as broadly useful as possible.<br />
<br />
# Canvas people to let them know this is happening after we have concrete proposals that they can think over and comment on.<br />
# Announce the working group somehow, e.g. via mailing list<br />
# Perhaps have a google doc or some other collaborative document to house the drafts of the above goals and roles.<br />
<br />
===Tasks:===<br />
Finally, we assigned each other tasks to perform:<br />
# Typing up the minutes (Vladimir)<br />
# Establishing a google doc or wiki (Vladimir)<br />
# Establishing a mailing list (Vladimir)<br />
# Contact other department stewards via TAA (Ben)<br />
# Send out a when2meet in early January to determine next meeting</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16330Graduate Algebraic Geometry Seminar2018-11-02T04:13:01Z<p>Sotirov: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov/David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner/Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| TBD]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=16263AMS Student Chapter Seminar2018-10-24T15:20:48Z<p>Sotirov: </p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: We will state what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that under certain nice conditions, the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=16260AMS Student Chapter Seminar2018-10-23T14:51:15Z<p>Sotirov: </p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: We will state what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that under certain nice conditions, the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, Vladimir Sotirov ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=16069AMS Student Chapter Seminar2018-09-25T15:19:14Z<p>Sotirov: </p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 10, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15215Graduate Algebraic Geometry Seminar Spring 20182018-03-07T19:06:13Z<p>Sotirov: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== 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 />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 14<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 14| Fun with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 21<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 21| <math>\mathcal F</math>un with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 28<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 28| ODEs: algebraic vs analytic vs formal]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Topology of Affine Schemes]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 21<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Spring break<br />
| bgcolor="#BCE2FE"| Whoo!<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Rachel Davis<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 18<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 18| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 2| TBD]]<br />
|}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Fun with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for D-modules on affine space, the Mellin transform, the Fourier-Mukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Z-action) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
|} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''<math>\mathcal F</math>un with commutative groups'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <math>\mathcal F</math>un with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: ODEs: algebraic vs analytic vs formal<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on D-modules, but it does not rely on the topics course.<br />
|} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Topology of Affine Schemes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
|} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15213Graduate Algebraic Geometry Seminar Spring 20182018-03-05T23:39:01Z<p>Sotirov: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== 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 />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 14<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 14| Fun with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 21<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 21| <math>\mathcal F</math>un with commutative groups]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 28<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 28| ODEs: algebraic vs analytic vs formal]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| Topology of Affine Schemes]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 21<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Spring break<br />
| bgcolor="#BCE2FE"| Whoo!<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| Rachel Davis<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 18<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 18| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 2| TBD]]<br />
|}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Fun with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for D-modules on affine space, the Mellin transform, the Fourier-Mukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Z-action) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
|} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''<math>\mathcal F</math>un with commutative groups'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <math>\mathcal F</math>un with commutative groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: ODEs: algebraic vs analytic vs formal<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on D-modules, but it does not rely on the topics course.<br />
|} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Topology of Affine Schemes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Abelian_Varieties_2018&diff=15153Abelian Varieties 20182018-02-19T20:20:05Z<p>Sotirov: </p>
<hr />
<div>== Overview ==<br />
This reading seminar will cover Kempf's "Complex Abelian Varieties and Theta Functions" book. Talks will be Mondays, 4:00-4:50 in Room B139.<br />
<br />
We can try to cover Chapters 1-7 and Chapter 11 and maybe some topics from the other chapters of Birkenhake and Lange's "Complex Abelian Varieties" as time permits.<br />
<br />
== Talk Schedule ==<br />
The following schedule might be adjusted as we go, depending on whether it seems too fast or not.<br />
<br />
Here is the [[https://www.math.wisc.edu/wiki/images/TOC.pdf Table of Contents]] of Kempf's book.<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | sections<br />
<br />
|-<br />
|February 7<br />
|Rachel Davis<br />
|1.1-1.3<br />
|-<br />
|February 12<br />
|Soumya Sankar<br />
|1.4-1.5<br />
|-<br />
|February 19<br />
|Michael Brown<br />
|2.1-2.2<br />
|-<br />
|February 26<br />
|Solly Parenti<br />
|2.3-2.4<br />
|-<br />
|March 5<br />
|Vladimir Sotirov<br />
|3.1-3.3<br />
|-<br />
|March 12<br />
|Moisés Herradón Cueto<br />
|3.4-3.6<br />
|-<br />
|March 19<br />
|Brandon Boggess<br />
|4<br />
|-<br />
|March 26<br />
|No meeting<br />
|Spring Break<br />
|-<br />
|April 2<br />
|Mao Li<br />
|5.1-5.3<br />
|-<br />
|April 9<br />
|TBD<br />
|5.3-5.5<br />
|-<br />
|April 16<br />
|TBD<br />
|6<br />
|-<br />
|April 23<br />
|TBD<br />
|7<br />
|-<br />
|April 30<br />
|TBD<br />
|11<br />
|-<br />
|May 7<br />
|TBD<br />
|???<br />
|-<br />
|}</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15044Graduate Algebraic Geometry Seminar Spring 20182018-02-06T22:41:43Z<p>Sotirov: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== 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 />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 14<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 21<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 28<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 28| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 7<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 14<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 21<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 28<br />
| bgcolor="#C6D46E"| Spring break<br />
| bgcolor="#BCE2FE"| Whoo!<br />
|-<br />
| bgcolor="#E0E0E0"| April 4<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 4| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 18<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 18| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 25<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 2<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 2| TBD]]<br />
|}<br />
</center><br />
<br />
<br />
<br />
== February 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
<br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13730Graduate Algebraic Geometry Seminar Fall 20172017-05-16T01:01:25Z<p>Sotirov: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry 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.<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 />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], 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 />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 3<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent, part 2 ]] <br />
|}<br />
</center><br />
<br />
== January 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%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 1<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 3<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having discussed Grothendieck topologies and an existence theorem for absolute products of families, we construct <math>\mathfrak{M}_{1,1}</math><br />
and give a convenient characterization of the line bundles on the moduli problem, finally proving that <math>\mathrm{Pic}(\mathfrak{M}_{1,1})=\mathbb Z/12</math><br />
. Our numinous and mystical journey towards this sublime result will make ample use of Grothendieck's generalized Hilbert 90. Facts you knew about sheaf cohomology of schemes will suddenly materialize in the context of sites.<br />
|} <br />
</center><br />
<br />
== April 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%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Adjoint functors rule your life<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: This talk is about adjoint functors. We will do examples!<br />
<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A gentle introduction to descent<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I'll give an elementary description of descent theory, mostly distilled from reading [https://arxiv.org/abs/math/0412512 Part I] of [http://www.maa.org/press/maa-reviews/fundamental-algebraic-geometry-grothendiecks-fga-explained FGA Explained].<br />
<br />
You can find a(n idealized) transcript of this talk and its sequel at [[File:IntroDescent1.pdf]]<br />
|} <br />
</center> <br />
<br />
== May 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A gentle introduction to descent, part 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I'll continue my elementary description of descent theory.<br />
<br />
You can find a(n idealized) transcript of this talk and its sequel at [[File:IntroDescent1.pdf]]<br />
<br />
<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=File:IntroDescent1.pdf&diff=13729File:IntroDescent1.pdf2017-05-16T00:55:35Z<p>Sotirov: Sotirov uploaded a new version of File:IntroDescent1.pdf</p>
<hr />
<div>(Idealized) transcript of April 26 2017 GAGS talk</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=File:IntroDescent1.pdf&diff=13717File:IntroDescent1.pdf2017-04-29T00:46:38Z<p>Sotirov: Sotirov uploaded a new version of File:IntroDescent1.pdf</p>
<hr />
<div>(Idealized) transcript of April 26 2017 GAGS talk</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13713Graduate Algebraic Geometry Seminar Fall 20172017-04-28T02:51:46Z<p>Sotirov: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry 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.<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 />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], 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 />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 3<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent, part 2 ]] <br />
|}<br />
</center><br />
<br />
== January 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%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 1<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 3<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having discussed Grothendieck topologies and an existence theorem for absolute products of families, we construct <math>\mathfrak{M}_{1,1}</math><br />
and give a convenient characterization of the line bundles on the moduli problem, finally proving that <math>\mathrm{Pic}(\mathfrak{M}_{1,1})=\mathbb Z/12</math><br />
. Our numinous and mystical journey towards this sublime result will make ample use of Grothendieck's generalized Hilbert 90. Facts you knew about sheaf cohomology of schemes will suddenly materialize in the context of sites.<br />
|} <br />
</center><br />
<br />
== April 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%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Adjoint functors rule your life<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: This talk is about adjoint functors. We will do examples!<br />
<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A gentle introduction to descent<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I'll give an elementary description of descent theory, mostly distilled from reading [https://arxiv.org/abs/math/0412512 Part I] of [http://www.maa.org/press/maa-reviews/fundamental-algebraic-geometry-grothendiecks-fga-explained FGA Explained].<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Transcript: https://www.math.wisc.edu/wiki/images/IntroDescent1.pdf<br />
|} <br />
</center> <br />
<br />
== May 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A gentle introduction to descent, part 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I'll continue my elementary description of descent theory.<br />
<br />
You can find a transcript of part 1 (with the rough plan for both talks) at https://www.math.wisc.edu/wiki/images/IntroDescent1.pdf<br />
<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=File:IntroDescent1.pdf&diff=13712File:IntroDescent1.pdf2017-04-28T02:45:38Z<p>Sotirov: (Idealized) transcript of April 26 2017 GAGS talk</p>
<hr />
<div>(Idealized) transcript of April 26 2017 GAGS talk</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13702Graduate Algebraic Geometry Seminar Fall 20172017-04-26T04:48:16Z<p>Sotirov: signed up to talk at the last minute</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry 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.<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 />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], 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 />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent ]] <br />
|}<br />
</center><br />
<br />
== January 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%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 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%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 1<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 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%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 3<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having discussed Grothendieck topologies and an existence theorem for absolute products of families, we construct <math>\mathfrak{M}_{1,1}</math><br />
and give a convenient characterization of the line bundles on the moduli problem, finally proving that <math>\mathrm{Pic}(\mathfrak{M}_{1,1})=\mathbb Z/12</math><br />
. Our numinous and mystical journey towards this sublime result will make ample use of Grothendieck's generalized Hilbert 90. Facts you knew about sheaf cohomology of schemes will suddenly materialize in the context of sites.<br />
|} <br />
</center><br />
<br />
== April 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%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Adjoint functors rule your life<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: This talk is about adjoint functors. We will do examples!<br />
<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 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%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A gentle introduction to descent<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I'll give an elementary description of descent theory, mostly distilled from reading [https://arxiv.org/abs/math/0412512 Part I] of [http://www.maa.org/press/maa-reviews/fundamental-algebraic-geometry-grothendiecks-fga-explained FGA Explained].<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_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>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Spring_2017&diff=13689Algebraic Geometry Seminar Spring 20172017-04-21T00:59:48Z<p>Sotirov: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in Van Vleck B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Fall 2016 | the previous semester]].<br />
<!--and for [[Algebraic Geometry Seminar Spring 2017 | the next semester]].---><br />
<!-- and for [[Algebraic Geometry Seminar | this semester]].---><br />
<br />
==Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2017 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|January 20<br />
|[http://math.mit.edu/~sraskin/ Sam Raskin (MIT)] <br />
|[[#Sam Raskin|W-algebras and Whittaker categories]]<br />
|Dima<br />
|-<br />
|January 27<br />
|[http://math.uchicago.edu/~nks/ Nick Salter (U Chicago)] <br />
|[[#Nick Salter|Mapping class groups and the monodromy of some families of algebraic curves]]<br />
|Jordan<br />
|-<br />
|March 3<br />
|[http://www.math.wisc.edu/~laudone/ Robert Laudone (UW Madison)]<br />
|[[#Robert Laudone|The Spin-Brauer diagram algebra]]<br />
|local (Steven)<br />
|-<br />
|March 10<br />
|[http://www.math.wisc.edu/~clement/ Nathan Clement (UW Madison)]<br />
|[[#Nathan Clement|Parabolic Higgs bundles and the Poincare line bundle]]<br />
|local<br />
|-<br />
|March 17<br />
|[http://www.math.wisc.edu/~hhuang235/ Amy Huang (UW Madison)]<br />
|[[#Amy Huang|Equations of Kalman varieties]]<br />
|local (Steven)<br />
|-<br />
|March 31<br />
|[http://www.perimeterinstitute.ca/people/jie-zhou Jie Zhou (Perimeter Institute)] <br />
|[[#Jie Zhou|Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function]]<br />
|Andrei<br />
|-<br />
|April 7<br />
|[https://www2.warwick.ac.uk/fac/sci/maths/people/staff/vladimir_dokchitser/ Vladimir Dokchitser (Warwick)] <br />
|[[#Vladimir Dokchitser|Arithmetic of hyperelliptic curves over local fields]]<br />
|Jordan<br />
|-<br />
|April 14<br />
|[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim (UW-Madison)]<br />
|[[#Laurentiu Maxim| Characteristic classes of complex hypersurfaces and multiplier ideals]]<br />
|local<br />
|-<br />
|April 21<br />
|Vladimir Sotirov<br />
|[[#Vladimir Sotirov|Cohomology of compactified Jacobians of singular curves]]<br />
|local<br />
|-<br />
|May 5<br />
|Qingyuan Jiang (Chinese University of Hong Kong)<br />
|[[#Qingyuan Jiang|Categorical Plücker formula and Homological Projective Duality]]<br />
|Andrei<br />
<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sam Raskin===<br />
<br />
'''W-algebras and Whittaker categories'''<br />
<br />
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and for its Langlands dual through a subtle construction.<br />
<br />
The purpose of this talk is threefold: 1) to introduce a ``stratification" of the category of modules for the affine W-algebra, 2) to prove an analogue of Skryabin's equivalence in this setting, realizing the categoryof (discrete) modules over the W-algebra in a more natural way, and 3) to explain how these constructions help understand Whittaker categories in the more general setting of local geometric Langlands. These three points all rest on the same geometric observation, which provides a family of affine analogues of Bezrukavnikov-Braverman-Mirkovic. These results lead to a new understanding of the exactness properties of the quantum Drinfeld-Sokolov functor.<br />
<br />
===Nick Salter===<br />
<br />
'''Mapping class groups and the monodromy of some families of algebraic curves'''<br />
<br />
In this talk we will be concerned with some topological questions arising in the study of families of smooth complex algebraic curves. Associated to any such family is a monodromy representation valued in the mapping class group of the underlying topological surface. The induced action on the cohomology of the fiber has been studied for decades- the more refined topological monodromy is largely unexplored. In this talk, I will discuss some theorems concerning the topological monodromy groups of families of smooth plane curves, as well as families of curves in CP^1 x CP^1. This will involve a blend of algebraic geometry, singularity theory, and the mapping class group, particularly the Torelli subgroup.<br />
<br />
===Robert Laudone===<br />
<br />
'''The Spin-Brauer diagram algebra'''<br />
<br />
Schur-Weyl duality is an important result in representation theory which states that the actions of <math>\mathfrak{S}_n</math> and <math>\mathbf{GL}(N)</math> on <math>\mathbf{V}^{\otimes n}</math> generate each others' commutants. Here <math>\mathfrak{S}_n</math> is the symmetric group and <math>\mathbf{V}</math> is the standard complex representation. In this talk, we investigate the Spin-Brauer diagram algebra, which arises from studying an analogous form of Schur-Weyl duality for the action of the spinor group on <math>\mathbf{V}^{\otimes n} \otimes \Delta</math>. Here <math>\mathbf{V}</math> is again the standard <math>N</math>-dimensional complex representation of <math>{\rm Pin}(N)</math> and <math>\Delta</math> is the spin representation. We will give a general construction of the Spin-Brauer diagram algebra, discuss its connection to <math>{\rm End}_{{\rm Pin}(N)}(V^{\otimes n} \otimes \Delta)</math> and time permitting we will mention some interesting properties of the algebra, in particular its cellularity.<br />
<br />
===Nathan Clement===<br />
<br />
'''Parabolic Higgs bundles and the Poincare line bundle'''<br />
<br />
We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank.<br />
I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces.<br />
By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces.<br />
One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators.<br />
When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.<br />
<br />
===Amy Huang===<br />
<br />
'''Equations of Kalman Varieties'''<br />
<br />
Given a subspace L of a vector space V, the Kalman variety consists of all matrices of V that have a nonzero eigenvector in L. We will discuss how to apply Kempf Vanishing technique with some more explicit constructions to get a long exact sequence involving coordinate ring of Kalman variety, its normalization and some other related varieties in characteristic zero. This long exact sequence is first conjectured by Sam in 2011. Time permitting we will also discuss how to extract more information from the long exact sequence including the minimal defining equations for Kalman varieties.<br />
<br />
===Jie Zhou===<br />
<br />
'''Gromov-Witten invariants of elliptic curves and moments of Weierstrass P-function'''<br />
<br />
I will talk about a joint work with Si Li on the computation of higher genus Gromov-Witten invariants of elliptic curves using mirror symmetry.<br />
<br />
The Gromov-Witten theory for elliptic curves is proved by Si Li, basing on the works of Bershadsky-Cecotti-Ooguri-Vafa and Costello-Li, to be equivalent to a quantum field theory on the mirror elliptic<br />
curve. Taking the Feynman graph integrals as the definition of the quantum field theory, I will explain the computations on the integrals (which are closely related to moments of the Weierstrass P-function). I will also discuss the quasi-modularity and the modular completion of the integrals. The Hodge-theoretic interpretations of all of these will also be explained.<br />
<br />
===Vladimir Dokchitser===<br />
<br />
'''Arithmetic of hyperelliptic curves over local fields'''<br />
<br />
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x).<br />
<br />
===Laurentiu Maxim===<br />
<br />
'''Characteristic classes of complex hypersurfaces and multiplier ideals'''<br />
<br />
I will discuss two different ways to measure the complexity of singularities of a (globally-defined) complex hypersurface. The first is derived via (Hodge-theoretic) characteristic classes of singular complex algebraic varieties, while the second is provided by the multiplier ideals. I will also point out a natural connection between these two points of view. (Joint work with Morihiko Saito and Joerg Schuermann.)<br />
<br />
===Vladimir Sotirov===<br />
<br />
'''Cohomology of compactified Jacobians of singular curves'''<br />
<br />
===Qingyuan Jiang===<br />
<br />
'''Categorical Plücker formula and Homological Projective Duality'''<br />
<br />
The talk will be based on the joint work with Prof. Conan Leung, and Mr. Ying Xie (arXiv:1704.01050). We will be mainly interested in the question of how derived categories of coherent sheaves of two varieties behave under intersections, and how they are related to that of the original varieties. <br />
<br />
For the study of derive categories of linear sections of projective varieties, Kuznetsov introduced the concept of Homological Projective Duality (HPD). Since its introduction, the HPD theory becomes one of the most powerful frameworks in the homological study of algebraic geometry. The main result (HPD theorem) of the theory gives complete descriptions of bounded derived categories of coherent sheaves of (dual) linear sections of HP-dual varieties. <br />
<br />
For general intersections beyond linear sections, we show same type results hold. More precisely, our results are twofold: <br />
i) Decomposition part. For any two varieties $X$, $T$ with maps to projective space $\mathbb{P}$ and Lefschetz decompositions, then there is a semiorthogonal decomposition of $D(X\times_{\mathbb{P}} T$ into ‘ambient’ part (contributions from ambient product $X \times T$) and ‘primitive’ part, as long as the fiber product $X\times_{\mathbb{P}} T$ has expected dimension; <br />
ii) Comparison part. If $Y$, $S$ are the respective HP-duals of $X$, $T$, then the ‘primitive’ parts of the derived categories of the two fiber products $D(X\times_{\mathbb{P}} T$ and $D(Y \times_{\mathbb{P} S)$ are equivalent, provided that the two pairs intersect properly. <br />
In the case when one pair of HP-dual varieties (say $(S,T)$) are given by dual linear subspaces, our method provides a more direct proof of the original HPD theorem.</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=File:Compact-openTalk.pdf&diff=8383File:Compact-openTalk.pdf2014-09-25T05:52:24Z<p>Sotirov: Sotirov uploaded a new version of &quot;File:Compact-openTalk.pdf&quot;</p>
<hr />
<div></div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=8382AMS Student Chapter Seminar2014-09-25T05:41:13Z<p>Sotirov: </p>
<hr />
<div>'''General Information''': AMS Student Chapter Seminar will take place on Wednesday at 3:30 in the 9th floor lounge area. Talks should be of interest to the general math community, and generally will not run longer than 30 minutes. Everyone is welcome to give a talk, please just sign up on this page. Alternatively we will also sign interested people up at the seminar itself. There will generally be bagel provided, although the snack may vary from week to week. <br />
<br />
To sign up please provide your name and a title. Abstracts are welcome but optional.<br />
<br />
==Fall 2014==<br />
<br />
==Wednesday, September 25, Vladimir Sotirov==<br />
<br />
<br />
Title: [[Media:Compact-openTalk.pdf|The compact open topology: what is it really?]]<br />
<br />
Abstract: The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition.</div>Sotirovhttps://www.math.wisc.edu/wiki/index.php?title=File:Compact-openTalk.pdf&diff=8381File:Compact-openTalk.pdf2014-09-25T05:37:13Z<p>Sotirov: </p>
<hr />
<div></div>Sotirov