Spaces, Functions and Numbers Seminar: Lee -- Distribution of the cokernels of random p-adic matrices

Spaces, Functions, Numbers Seminar 

Speaker: Jungin Lee, Ajou University 

Title: Distribution of the cokernels of random p-adic matrices 

Abstract: Cohen-Lenstra heuristics predicts the distribution of the class groups of a
random quadratic number field.  Motivated by the Cohen-Lenstra heuristics, Friedman
and Washington studied the distribution of the cokernels of random matrices over the
ring of p-adic integers.  This has been generalized in many directions, as well as some
applications to the distribution of random algebraic objects.  

In this talk, first we give an overview of random matrix theory over the ring of p-adic
integers.  After that, we explain how to prove the universality results for random
p-adic matrices using the moments of random groups, which is an analogue of the moments
of random variables.  We also investigate the distribution of the cokernels of random
p-adic matrices with given zero entries, based on the joint work with Dong Yeap Kang and
Myungjun Yu.