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.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
Tel. 703-993-1460, Fax. 703-993-1491