Number/Representation Theory

Let $A$ be a random $n$ by $n$ matrix over $\mathbb{Z}_p$ which is equidistributed with respect to the Haar measure. Friedman and Washington proved that the distribution of the cokernel of $A$ follows the Cohen-Lenstra distribution. In this talk, we introduce three possible ways to generalize their work. In particular, we discuss the following results:

1. Joint distribution of the cokernels $cok(P_1(A)), ... , cok(P_l(A))$ for polynomials $P_1(t), ... , P_l(t) \in \mathbb{Z}_p[t]$ under some mild conditions

2. Universality of the cokernel of a random Hermitian matrix over the ring of integers of a quadratic extension of $\mathbb{Q}_p$.

Join Zoom Meeting https://utoronto.zoom.us/j/86481023050

Meeting ID: 864 8102 3050 Passcode: talk