## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Is a "random" element in the mapping class group Pseudo-Anosov?

**Speaker:** Howard Masur

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

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

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Dave McClendon

**Contact email:** dmm@math.northwestern.edu

**Contact Phone:** 847-467-1298

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