Dynamics and Volume Entropy of surfaces

This is in the general areas of Dynamical Systems, Ergodic Theory, and Geometry and Topology. The plan is to study the volume entropy, i.e., the rate of growth of length of circles or volume of disks on the universal covrer and explore its properties (regularity, critical points, etc.) There is scope for proving new rigidity theorems and constructing Weil-Petersson type metrics on the moduli space.