Probability Theory for Random Groups Arising in Number Theory

Explore probability theory for random groups in number theory, topology, and combinatorics in this 48-minute lecture by Melanie Matchett Wood for the International Mathematical Union. Delve into the moment problem and universality theorems for distributions of random groups, including those conjectured in Cohen-Lenstra-Martinet heuristics for class groups of random number fields and Selmer groups of random elliptic curves. Examine known results, new findings, and applications in the field of finite and profinite group distributions. Gain insights into open problems and future research directions in this advanced mathematical presentation, with accompanying slides available for reference.