### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

NOVEMBER 15, 2019

**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.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491