Graduate Algebraic Geometry Seminar Spring 2022

When: 4:30-5:30 PM Thursdays

Where: VV B231

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

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.

Spring 2022 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.

Hilbert Schemes
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

Talks

Date	Speaker	Title
February 10	Everyone	Informal chat session
February 17	Asvin G
February 24	Yu Luo
March 3
March 10	Colin Crowley
March 24	Caitlyn Booms
March 31	Ruofan
April 7	Alex Hof
April 14	John Cobb
April 21	Connor Simpson
April 28	Karan	Using varieties to study polynomial neural networks
May 5

February 10

Everyone

Title: Informal chat session

Abstract: Bring your questions!

February 17

Asvin G

Karan

Title: Using varieties to study polynomial neural networks

Abstract: In this talk, I will exposit the work of Kileel, Trager, and Bruna in their 2019 paper "On the Expressive power of Polynomial Neural Networks". We will look at 1) what a polynomial neural network is and how we can interpret the output such networks as varieties, 2) why the dimension of this variety and the expressive power of this network are related, and 3) how the study of these varieties might tell us something about the architecture of the network.