Graduate Algebraic Geometry Seminar Spring 2022: Difference between revisions

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=== Fall 2021 Topic Wish List ===
=== Fall 2021 Topic Wish List ===
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.
* Stacks for Kindergarteners
* Motives for Kindergarteners
* Applications of Beilinson resolution of the diagonal, Fourier Mukai transforms in general
* Wth did June Huh do and what is combinatorial hodge theory?
* Computing things about Toric varieties
* Computing things about Toric varieties
* Reductive groups and flag varieties
* Reductive groups and flag varieties
* Introduction to arithmetic geometry -- what are some big picture ideas of what "goes wrong" when not over an algebraically closed field?
* Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"
* Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"
* Going from line bundles and divisors to vector bundles and chern classes
* Going from line bundles and divisors to vector bundles and chern classes  
* A History of the Weil Conjectures
* A History of the Weil Conjectures
* Mumford & Bayer, "What can be computed in Algebraic Geometry?"  
* Mumford & Bayer, "What can be computed in Algebraic Geometry?"  
Line 35: Line 30:
* Do Not Speak For/Over the Speaker
* Do Not Speak For/Over the Speaker
* Ask Questions Appropriately
* Ask Questions Appropriately
==Talks==
<center>
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"
|-
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''
|-
| bgcolor="#E0E0E0"| September 30
| bgcolor="#C6D46E"| Yifan Wei
| bgcolor="#BCE2FE"|[[#September 30| On Chow groups and K groups]]
|-
| bgcolor="#E0E0E0"| October 7
| bgcolor="#C6D46E"| Owen Goff
| bgcolor="#BCE2FE"|[[#October 7 | Roguish Noncommutativity and the Onsager Algebra]]
|-
| bgcolor="#E0E0E0"| October 14
| bgcolor="#C6D46E"| Peter Wei
| bgcolor="#BCE2FE"|[[#October 14 | TBD]]
|-
| bgcolor="#E0E0E0"| October 21
| bgcolor="#C6D46E"| Asvin G
| bgcolor="#BCE2FE"|[[#October 21 | Introduction to Arithmetic Schemes]]
|-
| bgcolor="#E0E0E0"| October 28
| bgcolor="#C6D46E"| Caitlyn Booms
| bgcolor="#BCE2FE"|[[#October 28 | TBD]]
|-
| bgcolor="#E0E0E0"| November 4
| bgcolor="#C6D46E"| John Cobb
| bgcolor="#BCE2FE"|[[#November 4 | Koszul Cohomology]]
|-
| bgcolor="#E0E0E0"| November 11
| bgcolor="#C6D46E"| Colin Crowley
| bgcolor="#BCE2FE"| [[#November 11 | Introduction to Geometric Invariant Theory]]
|-
| bgcolor="#E0E0E0"| November 18
| bgcolor="#C6D46E"| Connor Simpson
| bgcolor="#BCE2FE"|[[#November 18 | Combinatorial Hodge Theory]]
|-
| bgcolor="#E0E0E0"| December 2
| bgcolor="#C6D46E"| Alex Mine
| bgcolor="#BCE2FE"|[[#December 2 | Galois Descent]]
|-
| bgcolor="#E0E0E0"| December 9
| bgcolor="#C6D46E"| Yu Luo
| bgcolor="#BCE2FE"|[[#December 9 | Stacks for Kindergarteners]]
|}
</center>
=== September 30 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Yifan Wei'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: On Chow groups and K groups
|-
| bgcolor="#BCD2EE"  | 
Abstract:
We define Chow groups and K groups for non-singular varieties, illustrate some basic properties, and explain how intersection theory is done using K groups (on a smooth surface). Then we proceed to compute the K group of a non-singular curve. On higher dimensions there might be some issues, if time permits we will show how these issues can be mitigated, and why Grothendieck-Riemann-Roch is one of the greatest theorems in algebraic geometry (in my humble opinion).
|}                                                                       
</center>
=== October 7 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Owen Goff'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: Roguish Noncommutativity and the Onsager Algebra
|-
| bgcolor="#BCD2EE"  | 
Abstract:
While throughout algebraic geometry and many other fields we like commutative rings, we often wonder what happens if our ring is not commutative. Say, for instance, you have A^2, but instead of xy=yx you have a relation xy = qyx for some constant q. In this talk I will discuss the consequences of this relation and how it relates to an object of combinatorial nature called the q-Onsager algebra.
|}                                                                       
</center>
=== October 14 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: TBD
|-
| bgcolor="#BCD2EE"  | 
Abstract:
TBD
|}                                                                       
</center>
=== October 21 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: Introduction to Arithmetic Schemes
|-
| bgcolor="#BCD2EE"  | 
Abstract:
TBD
|}                                                                       
</center>
=== October 28 ===
<center>
{| 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="#BCD2EE"  align="center" | Title: TBD
|-
| bgcolor="#BCD2EE"  | 
Abstract:
TBD
|}                                                                       
</center>
=== November 4 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: Koszul Cohomology
|-
| bgcolor="#BCD2EE"  | 
Abstract:
Or something else, I'm not sure yet. <!-- or maybe that paper by Lazarsfeld about castelnuovo-mumford regularity, or if I'm being lazy the quot functor and moduli theory -->
|}                                                                       
</center>
=== November 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%" | '''Colin Crowley'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: Introduction to Geometric Invariant Theory
|-
| bgcolor="#BCD2EE"  | 
Abstract: TBD
|}                                                                       
</center>
=== November 18 ===
<center>
{| 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="#BCD2EE"  align="center" | Title: Combinatorial Hodge Theory
|-
| bgcolor="#BCD2EE"  | 
Abstract: TBD
|}                                                                       
</center>
=== December 2 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Mine'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: Galois Descent
|-
| bgcolor="#BCD2EE"  | 
Abstract:
TBD
|}                                                                       
</center>
=== December 9 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Yu Luo'''
|-
| bgcolor="#BCD2EE"  align="center" | Title: Stacks for Kindergarteners
|-
| bgcolor="#BCD2EE"  | 
Abstract: Brief introduction to stacks.
|}                                                                       
</center>


== Past Semesters ==
== Past Semesters ==

Revision as of 20:57, 18 October 2021

When: 5:00-6:00 PM Thursdays

Where: TBD

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. Sometimes people present an interesting paper they find. Other times people give a prep talk for the 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@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is here.

Organizers: John Cobb, Colin Crowley.

Give a talk!

We need volunteers to give talks this semester. If you're interested, please fill out this form. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the main page.

Fall 2021 Topic Wish List

This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.

  • Computing things about Toric varieties
  • Reductive groups and flag varieties
  • Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"
  • Going from line bundles and divisors to vector bundles and chern classes
  • A History of the Weil Conjectures
  • Mumford & Bayer, "What can be computed in Algebraic Geometry?"
  • A pre talk for any other upcoming talk

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

Past Semesters

Spring 2021

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

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