Mahler measure and manifoldsMPIM
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MPIM, Vivatsgasse, 7 - Lecture Hall
Max Planck Institute for Mathematics
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).