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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