Universal Distributions of Groups and Algebraic Objects

Explore the fascinating world of universal distributions in arithmetic statistics through this conference talk that examines the Cohen–Lenstra–Martinet heuristics and their implications for class groups of number fields. Delve into the concept of universal distributions on abelian groups and discover how these theoretical frameworks extend beyond traditional boundaries. Learn about current research findings and ongoing challenges in understanding the universality of distributions across various algebraic structures, including non-abelian groups, modules, and other mathematical objects that emerge in arithmetic statistics. Gain insights into the intersection of number theory and probability theory as the speaker presents both established results and open problems in this active area of mathematical research.