Mahler measure and manifolds

We will discuss how Mahler measure and related concepts (e.g., Salem numbers) are connected to problems about lengths of geodesics on
arithmetic hyperbolic manifolds. As a result, by solving problems using tools from analytic number theory, we are able to answer quantitative
questions in spectral geometry.

This talk will build towards two goals: (1) determining the proportion of Salem numbers produced by certain arithmetic hyperbolic lattices; (2)
showing that, on average, geodesic lengths of non-compact arithmetic hyperbolic orbifolds appear with high multiplicity. This talk is based on
joint work with various subsets of the following co-authors: Mikhail Belolipetsky (IMPA), Michelle Chu (U. Minnesota), Matilde Lalín (U.
Montréal), Plinio G. P. Murillo (U. Federal Fluminense), and Otto Romero (CIMAC).