Minerva Distinguished Visitor Lectures at Princeton University

Let $X$ be a complete hyperbolic metric on a surface of genus $g$ with $n$ punctures. In this lecture I will discuss the problem of the growth of $s^{k}_{X}(L)$, the number of closed curves of length at most $L$ on $X$ with at most $k$ self...

In the second lecture, I will discuss several natural geometric flows defined on bundles over the moduli spaces of curves. I will describe basic ergodic properties of these flows. I will discuss some open questions and some of the progress made in...

The first lecture will give some background on the geometry and dynamics on hyperbolic surfaces. I will give a brief overview of Teichmüller theory and properties of the mapping class groups and the space of geodesic currents. I will discuss some...