Title: The imaginary case of the nonabelian Cohen--Lenstra heuristics
Abstract: The Cohen-Lenstra heuristics predict the distribution of class groups of quadratic number fields. These conjectures are wide open, but nevertheless has been generalized in several different directions, including a non-abelian generalization by Liu, Wood, and Zureick-Brown replacing quadratic extensions with certain totally real Galois extensions and class groups with Galois groups of certain unramified extensions of global fields. In this talk, I will discuss an imaginary analogue of the work of Liu, Wood, and Zureick-Brown by providing the group presentation for these Galois groups that suggests the non-abelian Cohen-Lenstra heuristics in the imaginary case, and giving an idea of the proof of a weak version of these heuristics in the function field case. This work is joint with Yuan Liu.