Fall 2009

Given two conjugate mapping classes f and g, we produce a conjugating element w such that |w| ≤ K (|f| + |g|), where |·| denotes the word metric with respect to a fixed generating set, and K is a constant depending only on the generating set. As a consequence, the conjugacy problem for mapping class groups is exponentially bounded.

The first talk will review the concept of asymptotic dimension and some background material. In the second talk I will construct (many) actions of mapping class groups on quasi-trees, and show how this implies that mapping class groups have finite asymptotic dimension. This is joint work with Ken Bromberg and Koji Fujiwara.

The first talk will review the concept of asymptotic dimension and some background material. In the second talk I will construct (many) actions of mapping class groups on quasi-trees, and show how this implies that mapping class groups have finite asymptotic dimension. This is joint work with Ken Bromberg and Koji Fujiwara.

I will talk about line patterns in free groups and how they provide quasi-isometry invariants for mapping tori of linearly growing free group automorphisms. This is joint with Natasha Macura.

Let f be an isometry between spaces which are products of uniquely geodesic metric spaces with the sup norm. There are two obvious types of isometries from such a space to itself namely a permutation of the factor spaces and a product of isometries of the factor spaces. In this talk we will show that not only is the number of factor spaces an isometry invariant, but also that any isometry is a composition of the two isometries types mentioned above.

The Lipschitz metric on Outer Space is not symmetric. In fact d(x,y)/d(y,x) can be arbitrarily large. In joint work with Mladen Bestvina, we define a piecewise differentiable function \psi on Outer Space (which is invariant under the action of Out(Fn) and show that d(x,y) can be bounded in terms of d(y,x) and \psi(x) - \psi(y). I will discuss the proof of this theorem and some applications.

I'll explain why arithmetic groups of relative Q-type A_n, B_n, C_n, D_n, E_6, and E_7 satisfy an exponential isoperimetric inequality in some dimension.