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 Events
University of Alberta
Mon 7 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Rost nilpotence for surfaces
WMAX 110
Mon 7 Nov 2011, 3:10pm-4:10pm

Abstract

Let X be a smooth projective scheme over a field F. We say that Rost nilpotence is true for X in the category of Chow motives with integral coefficients if for any field extension E/F the kernel of 

CH_2(S x S)  --> CH_2(S_E x S_E)

consists of nilpotent correspondences. In my talk I will present a proof of Rost nilpotence for surfaces over fields of characteristic zero which uses Rost's theory of cycle modules.
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Daniel Moseley
University of Oregon
Mon 14 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Group actions on cohomology of varieties
WMAX 110
Mon 14 Nov 2011, 3:10pm-4:10pm

Abstract

This talk will explore a technique of using equivariant cohomology to say something about the action of a group on the cohomology of a space. In particular, we will look at examples of cohomology of flag varieties and configuration spaces. Also, we will look at a family of algebras with an algebro-geometric interpretation that admits an S_n action, and use the results we developed to make progress toward a result about these algebras.

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University of Toronto
Mon 21 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Coverings over tori and application to Klein's resolvent problem
WMAX 110
Mon 21 Nov 2011, 3:10pm-4:10pm

Abstract

Topological essential dimension of a covering is the minimal dimension of a base-space such that the original covering can be induced from some covering over this base-space.
 
We will see how to compute the topological essential dimension for coverings over tori.
 
Surprisingly this question turns out to be useful in obtaining estimates in Klein's resolvent problem: what is the minimal number k such that the equation z^n+a_1z^n+...+a_n=0 with complex coefficients a_1,...,a_n can be reduced by means of a rational substitution y=R(z,a_1,...,a_n) to an equation on y depending on k algebraically independent parameters.
 
We will also obtain some bounds in the analogue of this question for other algebraic functions and get a sharp result for functions on C^n unramified outside of coordinate hyperplanes.
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Northwestern University
Mon 28 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110
The quantum BCOV theory and higher-genus mirror symmetry
WMAX 110
Mon 28 Nov 2011, 3:10pm-4:10pm

Abstract

The physicists Bershadsky, Cecotti, Ooguri and Vafa argued that the mirror to the theory of Gromov-Witten invariants is provided by a certain quantum field theory on Calabi-Yau varieties.  I'll describe joint work in progress with Si Li, which gives a rigorous construction of the BCOV quantum field theory.  In the case of the elliptic curve, Li has shown that our theory recovers the Gromov-Witten invariants of the mirror curve, and so proving mirror symmetry in this example.

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