Algebra Seminar: Westerland -- Cohen-Lenstra heuristics for function fields and Hurwitz spaces

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.  

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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.  

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