International Seminar on Automorphic Forms

Lola Thompson (Utrecht University): Salem numbers and short geodesics

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 number theory, we are able to answer quantitative questions in spectral geometry. This talk will build towards two goals: showing that short geodesics on arithmetic hyperbolic surfaces are rare, and showing that, on average, geodesic lengths of non-compact arithmetic hyperbolic orbifolds appear with high multiplicity. This talk is based on joint work with Mikhail Belolipetsky, Matilde Lalín, and Plinio G. P. Murillo; and with Benjamin Linowitz, D. B. McReynolds, and Paul Pollack.

https://tu-darmstadt.zoom.us/j/68048280736