数学研究所

数学科学全国重点实验室

学术报告

数论研讨班

Speaker: 刘媛 助理教授（University of Illinois Urbana-Champaign ）

Inviter: 余红杰

Language: Chinese

Title: Distribution of Class Groups and Their Nonabelian Generalizations  ( 2 )

Time&Venue: 2025年7月22日（星期二）15:30-16:30& 晨兴110

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.