University of Alberta

Mon 7 Nov 2011, 3:10pm
Algebraic Geometry Seminar
WMAX 110

Rost nilpotence for surfaces

WMAX 110
Mon 7 Nov 2011, 3:10pm4:10pm
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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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, 3:10pm4:10pm
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 algebrogeometric 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, 3:10pm4:10pm
Abstract
Topological essential dimension of a covering is the minimal dimension of a basespace such that the original covering can be induced from some covering over this basespace.
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 highergenus mirror symmetry

WMAX 110
Mon 28 Nov 2011, 3:10pm4:10pm
Abstract
The physicists Bershadsky, Cecotti, Ooguri and Vafa argued that the mirror to the theory of GromovWitten invariants is provided by a certain quantum field theory on CalabiYau 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 GromovWitten invariants of the mirror curve, and so proving mirror symmetry in this example.
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