Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, November 29, 2021 - 12:00 to 12:50

Location:

Kidd 280 or contact Christine Escher or a zoom link.

Guest Speaker:

Stephen Wilson

Abstract:

If M is a k x n matrix for n > k, a _band_ in M is the k x k matrix formed by k consecutive columns of M; ‘consecutive’ is circular, so column 1 comes immediately after column n. Then M is ‘bandedly nonsingular’ provided that each of its n bands is nonsingular. Does such a matrix exist with entries from the numbers mod 2? We will first prove that for all n>k, such a matrix exists. We will then talk about why we want to know. The answer relates to a certain family of obnoxiously symmetric graphs called the raeger-Xu graphs. Some of them have a property called ‘being Cayley’ and some don’t. But all of them are quasi-Cayley provided that a bandedly nonsingular matrix of the right size exists. As it does.

Host: