Inkang Kim proved the non-arithmeticity of length spectra of rank-one locally symmetric spaces (i.e., they generate dense additive subgroups of real numbers). The non-arithmeticity has several important applications in geometry and dynamics, and remains open in many natural settings, including negatively curved Riemannian manifolds. In this talk, we consider covers of the moduli space of a Riemann surface and show that their Teichmüller length spectra are non-arithmetic. This is joint work with Inhyeok Choi.
