Graduate Algebraic Geometry Seminar Spring 2016

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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.


Spring 2016

Date Speaker Title (click to see abstract)
January 20 Jay Yang Tropical Geometry II
January 27 Jay Yang Tropical Geometry III
February 3 Ed Dewey Derived Category of Projective Space
February 10 Ed Dewey More Derived Category of Projective Space
February 17 TBD TBD
February 24 DJ Bruce Divisors and Stuff I
March 2 DJ Bruce Divisors and Stuff II
March 9 DJ Bruce Divisors and Stuff III
March 16 TBD TBD
March 23 N/A No GAGS This Week
March 30 Daniel Hast Jacobians, path integrals, and fundamental groups of curves I
April 6 Daniel Hast Jacobians, path integrals, and fundamental groups of curves II
April 13 Jason Steinberg Something Something Shimura Varieties
April 20 Quinton Westrich Projective Duality
April 27 Zachary Charles Polynomial systems, toric geometry, and Newton polytopes
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

Ed Dewey

Past Semesters

Fall 2015