Graduate Algebraic Geometry Seminar Fall 2017

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Wednesdays 1:30-2:30 pm, Room - TBA

The purpose of this seminar is to have a talk on each week by a graduate student to help orient ourselves for the Algebraic Geometry Seminar talk on the following Friday. These talks should be aimed at beginning graduate students, and could try to explain some of the background, terminology, and ideas for the grown-up AG talk that week, or can be about whatever you have been thinking about recently.

Give a talk!

We need volunteers to give talks this semester. If you're interested contact Nathan. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.

Fall 2012 Semester

Date Speaker Title (click to see abstract)
February 13 (Wed.) TBA TBA
February 20 (Wed.) Jeff Poskin Constructing proper but non-projective varieties.
February 27 (Wed.) TBA TBA
March 6 (Wed.) TBA TBA
March 13 (Wed.) TBA TBA
March 20 (Wed.) TBA TBA
March 27 (Wed.) Spring Break No Seminar
April 3 (Wed.) TBA TBA
April 10 (Wed.) Dima Arinkin Cartier duality for commutative algebraic groups
Time and room change: April 19 (Fri.), B305 Dima Arinkin Cartier duality: Part 2
April 24 (Wed.) TBA TBA
May 1 (Wed.) Andrew Bridy The Artin-Mazur zeta function of a rational map in positive characteristic".
May 8 (Wed.) TBA TBA


Soon!

Lalit Jain
Title: We Don't Need No Stinking Scheme

Abstract: Following Mumford, we'll compute the Picard group of the (non-existent) moduli space of elliptic curves.

February 13

TBA
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Abstract:

February 20

Jeff Poskin
Title: Constructing proper but non-projective varieties.

Abstract: It is known that, above dimension 1, there exist proper varieties that are not projective. Using the methods associated with the study of toric varieties, we give several examples and show why they must not be projective.

February 27

TBA
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Abstract:

March 6

TBA
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March 13

TBA
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March 20

TBA
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April 3

TBA
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April 10

Dima Arinkin
Title: Cartier duality for commutative algebraic groups

Abstract: The Cartier duality is an algebraic version of the Pontryagin duality. A finite commutative group may be viewed either as a locally compact group or as a discrete algebraic group. Accordingly, its dual can be interpreted in the topological way (the Pontryagin dual: the group of continuous characters to U(1)) or in the algebraic way (the Cartier dual: the group of regular characters to the multiplicative group). The Cartier duality extends to a beautiful and non-trivial correspondence on a wider class of affine commutative algebraic groups; this is similar to the extension of the Pontryagin duality from finite groups to locally compact groups.

April 19

Dima Arinkin
Title: Cartier duality II

Abstract: This is a continuation of my talk last week. The goal is to extend the Cartier duality to infinite commutative algebraic groups (and group ind-schemes). I will consider several examples, concluding with the one that is perhaps most spectacular: the Contou-Carrere symbol (the algebro-geometric version of the Hilbert symbol).

April 24

TBA
Title:

Abstract:

May 1

Andrew Bridy
Title: The Artin-Mazur zeta function of a rational map in positive characteristic".

Abstract: TBA

May 8

TBA
Title:

Abstract: