Videos

Michelle Chu - Salem numbers in arithmetic hyperbolic manifolds

October 12, 2026
Abstract
Salem numbers arise naturally from the lengths of closed geodesics in arithmetic hyperbolic manifolds. In this talk, we characterize when the logarithm of a Salem number occurs as the length of a closed geodesic in the commensurability class of an arithmetic hyperbolic manifold, in terms of its arithmetic data. We also show that a given Salem number can occur in infinitely many pairwise incommensurable arithmetic hyperbolic manifolds.