Title: Is a "random" element in the mapping class group Pseudo-Anosov?
Speaker: Howard Masur
Speaker Info: University of Chicago
Suppose S is a surface of genus g with n punctures. Let Mod(S) denote the mapping class group of S; the isotopy classes of homeomorphisms of S. In his famous classification, Thurston classfied elements of Mod(S) as finite order, reducible or Pseudo-Anosov. One can ask whether a "random" element is Pseudo-Anosov. This problem can be taken in several contexts. For example if one does a random walk on the group, what can ask for the probability that an element is Pseudo-Anosov. I will focus on a "lattice counting problem". Mod(S) acts properly by isometries on Teichmuller space with the Teichmuller metric. One takes the Mod(S) orbit of a given point that lie in larger and larger balls about the point. Then one counts how many orbit points there are and of which type. I will discuss what is known about this problem.Date: Tuesday, February 09, 2010