Graduate Algebraic Geometry Seminar Spring 2023

When: 4:15-5:15 PM on Fridays

Where: Van Vleck B119

Toby 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, Yu (Joey) Luo

Give a talk!

We need volunteers to give talks this semester. 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. Sign up here.

Wishlist

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
Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"
A History of the Weil Conjectures
A pre talk for any other upcoming talk
Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).

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
January 31	Mahrud Sayrafi	Bounding the Multigraded Regularity of Powers of Ideals
February 1	John Cobb	Introduction to Intersection Theory
February 3
February 10
February 17
February 24
March 3
March 10
March 24
March 31
April 7
April 14
April 21
April 28
May 5

January 31

Mahrud Sayrafi

Title: Bounding the Multigraded Regularity of Powers of Ideals

Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.

Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.