Presented by: 
Craig Westerland (University of Melbourne)
Date: 
Mon 18 Mar, 2:00 pm - 2:45 pm
Venue: 
Mansergh Shaw 45-204

Configuration spaces have a long history in topology and geometry, cropping up in areas as distinct as gravitation, robotics, and function spaces. In this talk, I'll give a brief introduction to these remarkable objects with an eye to their application in the topology of certain moduli spaces of branched covers of Riemann surfaces. The results can be applied to prove a form of the Cohen-Lenstra heuristics on the distribution of class groups. Traditionally stated in terms of the probability that a number field has a given group as its class group, a "function field" variant may be formulated in terms of enumeration of branched covers of surfaces of a certain form. This is joint work with Jordan Ellenberg and Akshay Venkatesh.