### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

APRIL 17, 2015

**Speaker: **
Lowell Abrams, George Washington University

**Title: ***
Cellular automorphisms of embedded graphs and two mathematical applications
*

**Abstract:**
I will begin by aquainting the audience with the notions of a cellular graph embedding in a surface, cellular automorphisms of embedded graphs, and a notion of "equivariant reduction" for embedded graphs which generalizes graph minors. I will then describe a catalog Dan Slilaty and I constructed of all irreducible cellular automorphisms of graphs in the sphere, projective plane, torus, Klein bottle, and 3-crosscaps surface. Finally, I will show how Dan Slilaty and I have applied this catalog to (1) the construction of self-dual graph embeddings, and (2) the identification of the minimal obstructions to embedding symmetric graphs in the sphere in such a way that the symmetry extends to the sphere.

**Time:** Friday, April 17, 2015, 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