Nonabelian Cohen-Lenstra Heuristics and Function Field Theorems

Athens-Atlanta Number Theory Seminar
Thursday, April 14, 2016 - 16:05
1 hour (actually 50 minutes)
Skiles 006
University of Wisconsin
The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields. Since, by class field theory, the class group is the Galois group of the maximal unramified abelian extension, we can consider the Galois group of the maximal unramified extension as a non-abelian generalization of the class group. We will explain non-abelian analogs of the Cohen-Lenstra heuristics due to Boston, Bush, and Hajir and joint work with Boston proving cases of the non-abelian conjectures in the function field analog.