Nonabelian Cohen-Lenstra heuristics and function field theorems

Joint IAS/Princeton University Number Theory Seminar
Topic:Nonabelian Cohen-Lenstra heuristics and function field theorems
Speaker:Melanie Wood
Affiliation:University of Wisconsin–Madison
Date:Thursday, November 17
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/puias/2016/1117-MelanieWood

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 work, some joint with Boston, proving cases of the non-abelian conjectures in the function field analog.