Graduate Algebraic Geometry Seminar Fall 2017

When: Wednesdays 4:00pm

Where:Van Vleck B139

Lizzie the OFFICIAL mascot of GAGS!!

Who: YOU!!

Why: The purpose of this seminar is to learn algebraic geometry 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.

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 DJ, 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.

Wish List

If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.

• Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)

• A careful explanation of the correspondence between graded modules and sheaves on projective varieties.

• Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things easier)

• Homological projective duality

• The orbit method (for classifying representations of a Lie group)

• Kaledin: geometry and topology of symplectic resolutions

• Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)

• Geometric complexity theory, maybe something like arXiv:1508.05788.

Fall 2016

Date	Speaker	Title (click to see abstract)
January 20	TBD	TBD
January 27	TBD	TBD
February 3	TBD	TBD
February 10	TBD	TBD
February 17	TBD	TBD
February 24	TBD	TBD
March 2	TBD	TBD
March 9	TBD	TBD
March 16	TBD	TBD
March 23	TBD	TBD
March 30	TBD	TBD
April 6	TBD	TBD
April 13	TBD	TBD
April 20	TBD	TBD
April 27	TBD	TBD
May 4	TBD	TBD
May 11	TBD	TBD

January 20

Jay Yang

Title: Tropical Geometry II

Abstract: Previously we discussed the basic definitions of tropical geometry, and the connection to algebraic geometry. Now we use this to count curves through points on P^2. This is a well known result initially proven without the use of tropical tools. But using tropical tools we can give a proof that relies on the combinatorics of lattice paths. I will begin with a review of some facts from tropical geometry that we need for this proof.

January 27

TBD

Title: TBD

Abstract: TBD

February 3

Ed Dewey

Title: Derived Category of Projective Space

Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the Skimming.

February 10

Ed Dewey

Title: More Derived Category of Projective Space

Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.

February 17

TBD

Title: TBD

Abstract: TBD

February 24

DJ Bruce

Title: Divisors and Stuff I

Abstract: TBD

March 2

DJ Bruce

Title: Divisors and Stuff II

Abstract: TBD

March 9

DJ Bruce

Title: Divisors and Stuff III

Abstract: TBD

March 16

TBD

Title: TBD

Abstract: TBD

March 23

No Seminar This Week

Title: N/A

Abstract: Enjoy your break!

March 30

Daniel Hast

Title: Jacobians, path integrals, and fundamental groups of curves I

Abstract: TBD

April 6

Daniel Hast

Title: Jacobians, path integrals, and fundamental groups of curves II

Abstract: TBD

April 13

Jason Steinberg

Title: Something Something Shimura Varieties

Abstract:

April 20

Quinton Westrich

Title: Projective Duality

Abstract: Intro to discriminants and duals of projective varieties. My field will be C.

April 27

Zachary Charles

Title: Polynomial systems, toric geometry, and Newton polytopes

Abstract: While the Bezout bound generically gives us the number of roots of a polynomial system in projective space, often much more can be said about specific systems in affine space. Kushnirenko's Theorem (and later Bernstein's theorem) gives better bounds for "sparse" systems of polynomials. These bounds are based on the volume of Newton polytopes. I will prove Kushnirenko's theorem using ideas from toric geometry, commutative algebra, and the geometry of polytopes. If time permits we will give applications of this theorem to power systems.

May 4

TBD

Title: TBD

Abstract: TBD

May 11

TBD

Title: TBD

Abstract: TBD

Organizers' Contact Info

DJ Bruce

Nathan Clement

Past Semesters

Spring 2016 Fall 2015