EVENT DETAILS AND ABSTRACT

Title: Lattice counting problems in the mapping class group
Speaker: Howard Masur
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

Let S be a closed surface of genus at least 1 and Mod(S) the mapping class group of S. This group is basic in the study of the geometry and topology of surfaces. There are various counting problems associated to the mapping class group. One of these problems, the lattice counting problem arises from the study of the action of Mod(S) on the Teichmuller space of S. This is the problem of counting the number of orbits of a point that lie in larger and larger balls. This counting was accomplished in a paper of Athreya, Bufetov, Eskin and Mirzakhani. They used dynamics in a fundamental way, inspired in part by the thesis of Margulis who studied the lattice counting problem for the action of the fundamental group of a compact negatively curved manifold on its universal cover. I will give some of this history including introducing the basic objects of study such as Teichmuller space, properties of the action, and how dynamics was used. I will then discuss more recent joint work with Spencer Dowdall where in the lattice counting problem we count the number of finite order and reducible elements in the mapping class group.