Graduate Algebraic Geometry Seminar Fall 2017

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Revision as of 17:01, 31 January 2016 by Dewey (talk | contribs) (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 Semiorthogonal Decomposition for Algebraic Varieties
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 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: Semiorthogonal Decomposition for Algebraic Varieties

Abstract: I will explain some results from Bondal and Orlov's article of the same name.

One interpretation of what it should mean to "compute" a triangulated category is to give a full exceptional sequence, or failing that a semiorthogonal decomposition into two categories that you are willing to pretend to understand. Bondal and Orlov did this for the intersection of two quadrics and for blowups. The strategy is to express one of the terms in the semiorthogonal decomposition as the image of a Fourier-Mukai transform. This is useful because they have a theorem (this is probably the "main content" of the paper) that lets you guarantee that the FM transform is full and faithful.

February 10

Ed Dewey
Title: Semiorthogonal Decompositions for Algebraic Varieties

Abstract: I will explain some results from Bondal and Orlov's article of the same name.

One interpretation of what it should mean to "compute" a triangulated category is to give a full exceptional sequence, or failing that a semiorthogonal decomposition into two categories that you are willing to pretend to understand. Bondal and Orlov did this for the intersection of two quadrics and for blowups. The strategy is to express one of the terms in the semiorthogonal decomposition as the image of a Fourier-Mukai transform. This is useful because they have a theorem (this is probably the "main content" of the paper) that lets you guarantee that the FM transform is full and faithful.

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

TBD
Title: TBD

Abstract: TBD

April 20

TBD
Title: TBD

Abstract: TBD

April 27

TBD
Title: TBD

Abstract: TBD

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