Graduate Algebraic Geometry Seminar Spring 2021

When: Thursday 5:00-6:00 PM CST

Where: https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09

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 Colin 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:

Schedule

February 4	Asvin Gothandaraman	A Bertini type theorem via probability
February 25	Colin Crowley	TBD
March 11	Roufan Jiang	TBD
March 18	Alex Hof	An Introduction to the Deformation Theory of Complete Intersection Singularities
March 25	Chiahui (Wendy) Cheng	Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials
April 1	Erika Pirnes	Reconstruction conjecture in graph theory (Note: special time at noon!)
April 8	Caitlyn Booms	TBD

February 4

Asvin Gothandaraman

Title: A Bertini type theorem via probability

Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary!

February 25

Colin Crowley

Title: TBD

Abstract: TDB

March 11

Roufan Jiang

Title: TBD

Abstract: TBD

March 18

Alex Hof

Title: An Introduction to the Deformation Theory of Complete Intersection Singularities

Abstract: Essentially what it says in the title; I'll give a fairly laid-back overview of some of the basic definitions and results about deformations of complete intersection singularities, including the Kodaira-Spencer map and the existence of versal deformations in the isolated case. If time permits, I'll discuss Morsification of isolated singularities. Very little background will be assumed.

March 25

Chiahui (Wendy) Cheng

Title: Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials

Abstract: Let f_1,...,f_r in k[x_1,...,x_n] be homogeneous polynomial of degree d. Ananyan and Hochster (2016) proved that there exists a bound N=N(r,d) where if collective strength of f_1,...,f_r is greater than or equal to N, then f_1,...,f_r are regular sequence. In this paper, we study the explicit bound N(r,d) when $r=3$ and d=2,3 and show that N(3,2)=2 and N(3,3)>2.

April 1

Erika Pirnes

Title: Reconstruction conjecture in graph theory (Note: special time at noon!)

Abstract: The deck of a graph with n vertices is a multiset of n unlabeled graphs, each obtained from the original graph by deleting a vertex (and the edges incident to it). The reconstruction conjecture says that if two finite simple graphs with at least three vertices have the same deck, then they are isomorphic. The talk is going to focus on examples, and does not assume previous knowledge about graph theory.