Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow

Artur Avila, Sebastien Gouezel

We consider the $SL(2,R)$ action on moduli spaces of quadratic differentials. If $\mu$ is an $SL(2,R)$-invariant probability measure, crucial information about the associated represe…