• Publications
  • Influence
Weil-Petersson volumes and intersection theory on the moduli space of curves
In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn,
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g \rightarrow \infty.$ We apply these asymptotic estimates to study
Counting closed geodesics in Moduli space
We compute the asymptotics, as R tends to infinity, of the number of closed geodesics in Moduli space of length at most R, or equivalently the number of pseudo-Anosov elements of the mapping class
Invariant and stationary measures for the SL(2,R) action on Moduli space
We prove some ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular
Counting Mapping Class group orbits on hyperbolic surfaces
Let $S_{g,n}$ be a surface of genus $g $ with $n$ marked points. Let $X$ be a complete hyperbolic metric on $S_{g,n}$ with $n$ cusps. Every isotopy class $[\gamma]$ of a closed curve $\gamma \in
Lattice Point Asymptotics and Volume Growth on Teichmuller space.
We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis (Mar70) to Teichmuller space. Let X be a point in Teichmuller space, and let BR(X) be the ball of radius R centered at X (with
Isolation, equidistribution, and orbit closures for the SL(2,R) action on Moduli space
We prove results about orbit closures and equidistribution for the SL(2,R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of
Ergodic Theory of the Space of Measured Laminations
We classify locally finite invariant measures and orbit closure for the action of the mapping class group on the space of measured laminations on a surface. This classification translates to a