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.

Department of Mathematical Sciences
George Mason University
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Fairfax, VA 22030-4444
http://math.gmu.edu/
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