Mathematics Colloquium: Decomposition Theorems for Cayley Graphs of Matrix Groups

Speaker: Jason Rosenhouse, James Madison University

Title: Decomposition Theorems for Cayley Graphs of Matrix Groups

Abstract: Cayley graphs of the projective special linear groups arise in a variety of contexts. For example: as the 1-skeletons of the Platonic solids and as graphs associated to triangulations of arithmetic Riemann surfaces. We will prove certain decomposition theorems for large classes of these graphs, and we will use these decompositions to find bounds on their Cheeger constants and eigenvalues. These results find applications in spectral geometry and number theory. To make the talk as self-contained as possible, we will also present some introductory material about algebraic graph theory in general. At least the first half of the talk should be accessible to students.

Time: Friday, November 15, 2019, 3:30-4:20 p.m.

Place: Exploratory Hall, room 4106

Refreshments will be served at 3:00 p.m.