Difference between revisions of "Graduate Algebraic Geometry Seminar"

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'''When:''' Wednesdays 4:25pm
 
'''When:''' Wednesdays 4:25pm
  
'''Where:''' Van Vleck B317 (Spring 2019)
+
'''Where:''' Van Vleck B317
 
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]
 
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]
  
Line 14: Line 14:
 
== Give a talk! ==
 
== Give a talk! ==
 
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.
 
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.
 +
  
 
== Being an audience member ==
 
== Being an audience member ==
Line 105: Line 106:
 
__NOTOC__
 
__NOTOC__
  
== Spring 2019 ==
+
== Fall 2019 ==
  
 
<center>
 
<center>
Line 114: Line 115:
 
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''
 
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''
 
|-
 
|-
| bgcolor="#E0E0E0"| February 6
+
| bgcolor="#E0E0E0"| September 18
| bgcolor="#C6D46E"| Vlad Sotirov
+
| bgcolor="#C6D46E"| David Wagner
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#September 12| M_g Potpourri]]
 +
|-
 +
| bgcolor="#E0E0E0"| September 25
 +
| bgcolor="#C6D46E"| TBD
 +
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#September 26| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| February 13
+
| bgcolor="#E0E0E0"| October 2
| bgcolor="#C6D46E"| David Wagner
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#October 3| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| February 20
+
| bgcolor="#E0E0E0"| October 9
| bgcolor="#C6D46E"| Caitlyn Booms
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#October 10| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| February 27
+
| bgcolor="#E0E0E0"| October 16
| bgcolor="#C6D46E"| Sun Woo Park
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#October 17| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| March 6
+
| bgcolor="#E0E0E0"| October 23
| bgcolor="#C6D46E"| Connor Simpson
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#October 24| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| March 13
+
| bgcolor="#E0E0E0"| October 30
| bgcolor="#C6D46E"| Brandon Boggess
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#October 31| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| March 27
+
| bgcolor="#E0E0E0"| November 6
| bgcolor="#C6D46E"| Solly Parenti
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#November 7| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| April 3
+
| bgcolor="#E0E0E0"| November 13
| bgcolor="#C6D46E"| Colin Crowley
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#November 14| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| April 10
+
| bgcolor="#E0E0E0"| November 20
| bgcolor="#C6D46E"| Alex Hof
+
| bgcolor="#C6D46E"| Caitlyn Booms
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#November 21| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| April 17
+
| bgcolor="#E0E0E0"| November 28
| bgcolor="#C6D46E"| Soumya Sankar
+
| bgcolor="#C6D46E"| Thanksgiving Break
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#November 30| ]]
 
|-
 
|-
| bgcolor="#E0E0E0"| April 24
+
| bgcolor="#E0E0E0"| December 4
| bgcolor="#C6D46E"| Name
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#December 5| Title TBD]]
 
|-
 
|-
| bgcolor="#E0E0E0"| May 1
+
| bgcolor="#E0E0E0"| December 11
| bgcolor="#C6D46E"| Shengyuan Huang
+
| bgcolor="#C6D46E"| TBD
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar Fall 2018#December 12| Title TBD]]
 
|}
 
|}
 
</center>
 
</center>
  
== February 6 ==
+
== September 18 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''
 
|-
 
|-
| bgcolor="#BCD2EE" | Title: Heisenberg Groups and the Fourier Transform
+
| bgcolor="#BCD2EE"  align="center" | Title: M_g Potpourri
 
|-
 
|-
 
| bgcolor="#BCD2EE"  |   
 
| bgcolor="#BCD2EE"  |   
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.
+
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.
  
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== February 13 ==
+
== September 25 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE"  | Title: Classification of TFT's
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques.
+
| bgcolor="#BCD2EE"  |  
[[File:Dg-meme.png]]
+
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== February 20 ==
+
== October 2 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE"  | Title: Completions of Noncatenary Local Domains and UFDs
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== February 27 ==
+
== October 9 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE"  | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== March 6 ==
+
== October 16 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE" | Title:
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== March 13 ==
+
== October 23 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE" | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== March 27 ==
+
== October 30 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE" | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== April 3 ==
+
== November 6 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE" | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== April 10 ==
+
== November 13 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE"  | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== April 17 ==
+
== November 20 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''
 
|-
 
|-
| bgcolor="#BCD2EE" | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== April 24 ==
+
== November 28 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Thanksgiving Break'''
 
|-
 
|-
| bgcolor="#BCD2EE"  | Title:  
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:  
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== May 1 ==
+
== December 4 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 
|-
 
|-
| bgcolor="#BCD2EE"  | Title: Orbifold Singular Cohomology
+
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
|-
| bgcolor="#BCD2EE"  | Abstract:  
+
| bgcolor="#BCD2EE"  |  
 +
Abstract:
 +
 
 +
|}                                                                       
 +
</center>
 +
 
 +
== December 11 ==
 +
<center>
 +
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 +
|-
 +
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
 +
|-
 +
| bgcolor="#BCD2EE"  align="center" | Title:
 +
|-
 +
| bgcolor="#BCD2EE"  | 
 +
Abstract:
 +
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
 
== Organizers' Contact Info ==
 
== Organizers' Contact Info ==
 +
  
 
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]
 
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]
Line 317: Line 358:
 
[http://www.math.wisc.edu/~drwagner/ David Wagner]
 
[http://www.math.wisc.edu/~drwagner/ David Wagner]
  
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]
 
  
 
== Past Semesters ==
 
== Past Semesters ==
 +
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]
 +
 
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]
 
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]
  

Latest revision as of 12:20, 18 September 2019

When: Wednesdays 4:25pm

Where: Van Vleck B317

Lizzie the OFFICIAL mascot of GAGS!!

Who: All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.

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.

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 here.

Give a talk!

We need volunteers to give talks this semester. If you're interested contact Caitlyn or 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.


Being an audience member

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:

  • Do Not Speak For/Over the Speaker:
  • Ask Questions Appropriately:

The List of Topics that we Made February 2018

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:

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.

  • 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!
  • 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.
  • Katz and Mazur explanation of what a modular form is. What is it?
  • Kindergarten moduli of curves.
  • 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?
  • Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)
  • Hodge theory for babies
  • What is a Néron model?
  • What and why is a dessin d'enfants?
  • DG Schemes.


Ed Dewey's Wish List Of Olde

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.

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.

Specifically Vague Topics

  • 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.
  • 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)

Famous Theorems

Interesting Papers & Books

  • Symplectic structure of the moduli space of sheaves on an abelian or K3 surface - Shigeru Mukai.
  • Residues and Duality - Robin Hatshorne.
    • 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 ;).)
  • Coherent sheaves on P^n and problems in linear algebra - A. A. Beilinson.
    • 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.)
  • Frobenius splitting and cohomology vanishing for Schubert varieties - V.B. Mehta and A. Ramanathan.
    • 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!
  • Schubert Calculus - S. L. Kleiman and Dan Laksov.
    • An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!
  • Rational Isogenies of Prime Degree - Barry Mazur.
    • 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.
  • Esquisse d’une programme - Alexander Grothendieck.
    • 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.)
  • Géométrie algébraique et géométrie analytique - J.P. Serre.
    • 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.)
  • Limit linear series: Basic theory- David Eisenbud and Joe Harris.
    • 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.
  • Picard Groups of Moduli Problems - David Mumford.
    • This paper is essentially the origin of algebraic stacks.
  • The Structure of Algebraic Threefolds: An Introduction to Mori's Program - Janos Kollar
    • 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.
  • Cayley-Bacharach Formulas - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.
    • 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?.
  • On Varieties of Minimal Degree (A Centennial Approach) - David Eisenbud and Joe Harris.
    • 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.
  • The Gromov-Witten potential associated to a TCFT - Kevin J. Costello.
    • 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.)


Fall 2019

Date Speaker Title (click to see abstract)
September 18 David Wagner M_g Potpourri
September 25 TBD Title TBD
October 2 TBD Title TBD
October 9 TBD Title TBD
October 16 TBD Title TBD
October 23 TBD Title TBD
October 30 TBD Title TBD
November 6 TBD Title TBD
November 13 TBD Title TBD
November 20 Caitlyn Booms Title TBD
November 28 Thanksgiving Break
December 4 TBD Title TBD
December 11 TBD Title TBD

September 18

David Wagner
Title: M_g Potpourri

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.

September 25

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October 2

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October 9

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October 16

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October 23

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October 30

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November 6

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November 13

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November 20

Caitlyn Booms
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November 28

Thanksgiving Break
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December 4

TBD
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December 11

TBD
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Organizers' Contact Info

Caitlyn Booms

David Wagner


Past Semesters

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015