Howard Masur

Large scale geometry of Teichmuller space

Abstract: One theme in Teichmuller theory and the mapping class group is the extent to which the space and the group exhibit the same properties as higher rank spaces and lattices and to the extent they exhibit properties of rank one spaces and lattices. We begin to explore this theme in the context of large scale or quasi-isometric geometry. Our work, joint with Jeff Brock focuses on the quasi-isometric rank of Teichmuller space with the Weil-Petersson metric.