The Cohen-Lenstra heuristics provide conjectures on the distribution of Class groups of quadratic number fields. We are a long way from proving these heuristics, but nevertheless the conjecture has been generalized in several different directions. A nonabelian version of the Cohen-Lenstra heuristics was first stated by Boston, Bush, and Hajir, which studied distributions of pro-p quotients of the Galois group of the maximal unramified extension of quadratic fields. Later, Liu, Wood, and Zureick-Brown stated a conjecture replacing the quadratic extension with totally real Galois extensions (with fixed Galois group). In this talk, I will try to give an idea of how a non-abelian Cohen-Lenstra heuristics can be developed for totally imaginary Galois extensions, and some evidence for why such a conjecture should hold.
Talk by Ken Willyard.