Mahler measures: from small heights to big conjectures - 4

by Riccardo Pengo

Friday 22 Mar 2024, 11:00 → 12:00 Europe/Zurich

Sitzungszimmer (MI)

The Mahler measure of a polynomial, defined as its geometric average over the unit torus, is a simple yet ubiquitous invariant, which appears in many different areas of mathematics. For example, it can be used as a measure of the complexity of the hypersurface cut out by the polynomial. It also allows one to compute the entropy of any action of a power of the additive group of the integers on a compact abelian group. Moreover, the Mahler measure of Alexander polynomials can be used to determine the asymptotic growth of homology in towers of knots, and similar results hold true for towers of finite graphs. Finally, Mahler measures of multivariate polynomials appear to be related to special values of L-functions. The aim of this minicourse is to provide an introduction to these (very) different areas in which Mahler measures make an appearance, with the hope of connecting the central themes of this workshop.