Commuting Graphs of p-adic Matrices by Ralph Morrison, Williams College

Commuting graphs of p-adic matrices by Ralph Morrison, Williams College, Friday October 4, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Faculty Seminar

Abstract:  The n x n commuting graph over a field k has all n x n nonscalar matrices with entries in k as its vertices, with two vertices connected by an edge when they commute under matrix multiplication.  When connected, the commuting graph is known to have diameter 4, 5, or 6.  In this talk I’ll present the first known example of a diameter-6 commuting graph that doesn’t rely on the axiom of choice:  the 14×14 commuting graph over the field of 2-adic numbers!