Coordinates: JH Michell Theatre in the Richard Berry Building
Speaker: Thang Le (Georgia Institute of Technology)
Title: Homology growth, volume, and Mahler measure
Abstract: We discuss the growth rate of homology torsions of finite coverings of knot and link complements. We prove a conjecture of K. Schmidt in algebraic dynamical system theory on the growth of the number of components of fixed point sets and a related conjecture of Silver and Williams on the growth of homology torsions of finite abelian covering of link complements. In both cases, the growth is expressed by the Mahler measure of the first non-zero Alexander polynomial of the corresponding modules.