When: 4:155:15 PM on Wednesday.
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 indepth. 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@ggroups.wisc.edu by sending an email to gags+subscribe@ggroups.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 8

Yiyu Wang

An introduction to Macpherson's Chern classes

February 15

Alex Hof

Normal Cones in Algebraic Geometry

February 22

Maya Banks

Syzygies of Projective Varieties

March 1

Asvin G

TBD

March 8



March 22

Kevin Dao

EnriquesKodaira Classification and its Influence on MMP

March 29

Peter Yi Wei

TBD

April 5

Colin Crowley (Maybe)

TBD

April 12

Yunfan He

Introduction to the DeligneIllusie theory

April 19

Jacob Wood

KTheory or something

April 26

Dima Arinkin

To be decided

May 3

Sun Woo Park

Introduction to Newton Polygon

January 31
Mahrud Sayrafi

Title: Bounding the Multigraded Regularity of Powers of Ideals

Abstract: Building on a result of Swanson, CutkoskyHerzogTrung and Kodiyalam described the surprisingly predictable asymptotic behavior of CastelnuovoMumford 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.

February 1
John Cobb

Title: Introduction to Intersection Theory

Abstract: In this advertisement talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me.

February 8
Yiyu Wang

Title: An introduction to Macpherson's Chern classes

Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.

February 15
Alex Hof

Title: Normal Cones in Algebraic Geometry

Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.

February 22
Maya Banks

Title: Syzygies of Projective Varieties

Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kickstarted this idea, such as CastelnuovoMumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examplesin particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.

March 1
Asvin G

Title: TBD

Abstract:

March 8
March 22
Kevin Dao

Title: EnriquesKodaira Classification and its Influence on MMP

Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (nonalgebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.

March 29
Peter Yi Wei

Title: TBD

Abstract:

April 5
Colin Crowley (Maybe)

Title: TBD

Abstract:

April 12
Yunfan He

Title: Introduction to the DeligneIllusie theory

Abstract:

April 19
Jacob Wood

Title:

Abstract:

April 26
May 3
Sun Woo Park

Title: Introduction to Newton Polygon

Abstract:

Past Semesters
Fall 2022
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