Maass cusp forms for Hecke triangle groups, closed geodesics, and invariant measures Abstract: Maass cusp forms are certain eigenfunctions of the Laplace-Beltrami operator which are of particular interest in number theory and physics. If $H$ denotes the upper half plane and $\Gamma$ is a Hecke triangle group, then the length spectrum of closed geodesics on $\Gamma\backslash H$ is generated by the Selberg zeta function. The Selberg trace formula shows that the zeros of the Selberg zeta function and the eigenvalues of Maass cusp forms are in bijection. For the Hecke triangle group $\PSL(2,\Z)$ combination of work by D. Mayer, and Lewis and Zagier provides an explicit isomorphism between Maass cusp forms and eigenfunctions of a transfer operator (evolution operator) which arises from a symbolic dynamics for the geodesic flow on $\PSL(2,\Z)\backslash H$. These eigenfunctions encode, via the Fredholm determinant of the transfer operator, the zeros of the Selberg zeta function. As a by-product, they prove the relation between zeros and eigenvalues avoiding the Selberg trace formula. I will report on work in progress joint with Martin Möller towards a uniform generalization of this so-called transfer operator method to all cofinite Hecke triangle groups.