Speaker: Prof. Yuan Liu (University of Illinois Urbana-Champaign)
Time: 14:00-16:30  July 22nd, 2025 (Tuesday)
Venue: MCM110

Title: Distribution of Class Groups and Their Nonabelian Generalizations

Abstract: A central question in arithmetic statistics is to understand the distribution of class groups across families of global fields. This line of inquiry began with the influential 1984 conjectures of Cohen and Lenstra, which predict the distribution of the odd part of class group of quadratic fields. Over the past two decades, significant progress has been made in various directions, including the proof of function field analogues of the Cohen–Lenstra heuristics, the study of nonabelian generalizations of class groups, and the exploration of how these distributions vary across different families of global fields. In this talk, I will survey the history and recent developments surrounding the (nonabelian) Cohen–Lenstra heuristics.