Yifeng Huang, USC 

Title: Cohen--Lenstra flag universality for random matrix products

Abstract: (Joint with Roger Van Peski and Hoi Nguyen) Abelian p-groups give a rich source of combinatorics, from q-analogues of binomial coefficients to q-analogues of Schur functions, e.g., Hall--Littlewood functions. An important direction in the theory of discrete random matrices is to model combinatorially interesting probability distributions of abelian p-groups by random matrices in (p-adic) integers. In this talk, I explain how a random matrix product model gives a random "flag" of groups distributed by the "Cohen—Lenstra" measure, in a "universal", robust way in that the resulting distribution is insensitive to the distribution of the matrix entries.