In this paper, we establish a relationship between the Weil-Petersson volume Vg,n(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b1, . . .â€¦ (More)

In the thick part of the moduli space of Riemann surface, we show the sectional curvature of the Weil-Petersson metric is bounded independent of the genus of the surface.

In this paper, we investigate the geometric properties of random hyperbolic surfaces of large genus. We describe the relationship between the behavior of lengths of simple closed geodesics on aâ€¦ (More)

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 ofâ€¦ (More)

We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis [Mar70] to TeichmÃ¼ller space. Let X be a point in TeichmÃ¼ller space, and let BR(X) be the ball of radius R centered at X (withâ€¦ (More)

Let Mg denote the moduli space of Riemann surfaces of genus g. We may write Mg = Tg/Î“, where Tg is the TeichmÃ¼ller space of genus g surfaces, and Î“ is the mapping class group. Let N(R) denote theâ€¦ (More)

the subgroup of diffeomorphisms homotopic to the identity map. It acts naturally on the space ML(S) of compactly supported measured laminations on S: a piecewise linear space associated to S, whoseâ€¦ (More)

In this paper we investigate the dynamics of the earthquake flow defined by Thurston on the bundle PMg of geodesic measured laminations. This flow is a natural generalization of twisting along simpleâ€¦ (More)