Difference between revisions of "Graduate Algebraic Geometry Seminar Fall 2017"

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(Fall 2016)
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Abstract: TBD
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Abstract: Enough with the algebra! Away with the schemes and categories! Consider a differential equation with some singularities, such as y'=1/x. Analysis tells us that its solutions can be extended along paths on the complex plane, but when a path loops around the singular point, 0 in this case, the solution might change. This phenomenon is called monodromy. Hilbert's twenty-first problem asks about the possible inverse of the monodromy construction: if some monodromy is prescribed on the plane with some points removed, is there a nice (Fuchsian), linear differential equation whose solutions have this monodromy? Attempting to solve this problem will quickly take us back to our cozy algebraic geometry world of sheaves and vector bundles. For those of us to whom the word sheaves produces a cold sweat running down our backs, this topic is a great way to motivate and introduce sheaves, and will ultimately give us a reason to care about nontrivial vector bundles.
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No knowledge (or ignorance) of sheaves is required and the analysis in the talk will be contained in the tiny amount that I myself know.
 
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Revision as of 14:53, 19 September 2016

When: Wednesdays 4:00pm

Where:Van Vleck B321 (Updated Fall 2016)

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)
September 14 DJ Bruce Vignettes in Algebraic Geometry
September 21 Moisés Herradón Cueto Hilbert's 21 and The Riemann-Hilbert correspondence
September 28 Moisés Herradón Cueto Hilbert's 21 and The Riemann-Hilbert correspondence
October 5 n/a No Seminar Today.
October 12 Nathan Clement TBD
October 19 Nathan Clement TBD
October 26 TBD TBD
November 2 TBD TBD
November 9 TBD TBD
November 16 TBD TBD
November 23 n/a No Seminar
November 30 DJ Bruce TBD
December 7 DJ Bruce TBD
December 14 TBD TBD

September 14

DJ Bruce
Title: Vignettes In Algebraic Geometry

Abstract:

Algebraic geometry is a massive forest, and it is often easy to become lost in the thicket of technical detail and seemingly endless abstraction. The goal of this talk is to take a step back out of these weeds, and return to our roots as algebraic geometers. By looking at three different classical problems we will explore various parts of algebraic geometry, and hopefully motivate the development of some of its larger machinery. Each problem will slowly build with no prerequisite assumed of the listener in the beginning.

September 21

Moisés Herradón Cueto
Title: Hilbert's 21 and The Riemann-Hilbert correspondence

Abstract: Enough with the algebra! Away with the schemes and categories! Consider a differential equation with some singularities, such as y'=1/x. Analysis tells us that its solutions can be extended along paths on the complex plane, but when a path loops around the singular point, 0 in this case, the solution might change. This phenomenon is called monodromy. Hilbert's twenty-first problem asks about the possible inverse of the monodromy construction: if some monodromy is prescribed on the plane with some points removed, is there a nice (Fuchsian), linear differential equation whose solutions have this monodromy? Attempting to solve this problem will quickly take us back to our cozy algebraic geometry world of sheaves and vector bundles. For those of us to whom the word sheaves produces a cold sweat running down our backs, this topic is a great way to motivate and introduce sheaves, and will ultimately give us a reason to care about nontrivial vector bundles.

No knowledge (or ignorance) of sheaves is required and the analysis in the talk will be contained in the tiny amount that I myself know.

September 28

Moisés Herradón Cueto
Title: Hilbert's 21 and The Riemann-Hilbert correspondence

Abstract: TBD

October 5

TBD
Title: TBD

Abstract: TBD

October 12

TBD
Title: TBD

Abstract: TBD


October 19

TBD
Title: TBD

Abstract: TBD

October 26

TBD
Title: TBD

Abstract: TBD

November 2

TBD
Title: TBD

Abstract: TBD

November 9

TBD
Title: TBD

Abstract: TBD

November 16

TBD
Title: TBD

Abstract: TBD


November 23

No Seminar This Week
Title: Enjoy Thanksgiving!

Abstract: n/a

November 30

TBD
Title: TBD

Abstract: TBD


December 7

TBD
Title: TBD

Abstract: TBD

December 14

TBD
Title: TBD

Abstract: TBD

Organizers' Contact Info

DJ Bruce

Nathan Clement


Past Semesters

Spring 2016

Fall 2015