Algebraic Geometry Seminar (note unusual time!)
Wednesday, November 11, 2009, 4:15pm, 119 Physics
Jordan Ellenberg (University of Wisconsin)
Stable cohomology for Hurwitz spaces
Abstract:- Hurwitz spaces are moduli spaces of finite branched covers of P1. We
will discuss the stabilization of the cohomology of these spaces as
the number of branch points grows, with the Galois group of the cover
being fixed; this can be thought of as a "Harer theorem" for this
family of moduli space. It turns out that the function field analogues
of many popular conjectures in analytic number theory (due to
Cohen-Lenstra, Bhargava, etc.) reduce to topological questions about
Hurwitz spaces. We will discuss the arithmetic consequences of the
stabilization theorem, and of a geometrically natural conjecture about
the stable cohomology classes of Hurwitz spaces. (joint work with
Akshay Venkatesh and Craig Westerland)
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