Type: Seminar

Distribution: World

Expiry: 18 Mar 2011

Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

The next algebra seminar will be given by Craig Westerland on Friday 18 March. Following the seminar we will take Craig to lunch, leaving from the 2nd floor of Carslaw at 1pm. --------------------------------------------------------------------- Speaker: Craig Westerland (University of Melbourne) Date: Friday 18th March Time: 12.05-12.55pm Venue: Carslaw 175 Title: Cohen-Lenstra heuristics for function fields and Hurwitz spaces Abstract: The Cohen-Lenstra heuristics are a family of (open) conjectures about the distribution of class groups of number fields (recall that the class group of a field measures the failure of its ring of integers to satisfy unique factorization). The analogous question for function fields asks for the distribution of class groups associated to branched coverings of curves in positive characteristic. Joint with Ellenberg and Venkatesh, we resolved this conjecture in the simplest case, corresponding to the setting of quadratic extensions. Remarkably, one can reduce this counting problem to an asymptotic computation of the homology of various Hurwitz moduli spaces of branched coverings. I’ll talk about the setup of the problem, and how we went about computing those homology groups. ---------------------------------------------------------------------