Department of Mathematics

Speaker: Susan Williams
Title: Periodic Graphs, Spanning Trees and Mahler Measure
Affiliation: University of South Alabama
Date: Thursday, March 3, 2016
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Infinite periodic graphs, graphs that are invariant under translation in one or more independent directions, are of interest in crystallography and statistical mechanics. One measure of complexity for such a graph is the spanning tree entropy, the exponential growth rate of the number of spanning trees in a sequence of finite subgraphs approximating the whole graph. This entropy has been calculated using mainly combinatoric and analytic arguments.

Using ideas of algebraic dynamics, we give a simplified approach to showing that the spanning tree entropy is the Mahler measure of a Laplacian polynomial that is easily obtained from graph data. Our work has applications to knot theory.

(Joint work with Daniel Silver)