Back to WTC Summer 2006

Peter Brinkmann

Anna Lenzhen
Teichmuller geodesics that do not have a limit in PMF
We construct a Teichmuller geodesics which does not have a limit on the Thurston boundary of Teichmuller space.

Lars Louder

Soren Galatius
Stable homology of automorphisms of free groups
The homology H_k(Aut(F_n)) of the automorphism group of a free group is known to be independent of n, as long as n > 2k+1. I will explain how to determine the homology in this stable range. The answer is that the homology agrees with the homology of the space QS^0, i.e. the direct limit of the n-fold loop space of the n-sphere, as n goes to infinity. The proof uses graphs and outer space, and is homotopy theoretic in flavor.

Howard Masur
Ergodic theory of translation surfaces
Let X be a closed Riemann surface and omega a holomorphic 1 form on X. The pair (X, \omega) defines the structure of a translation surface. This structure is equivalent to one htat is given by a collection of polygons in the plane that are glued along their boundaries by translations. for each direction theta, there is a flow in direction theta by straight lines on the surface. In genus one this gives the well known linear flow on the torus. In higher genus there are many additional interesting phenomena. This talk will survey what is known about the topological properties and ergodic theory of these flows.

Alexandra Pettet

Ben Schmidt

Blocking light in compact Reimannian manifolds
(Joint with J. Lafont) To what extent does the collision of light determine the geometry of space? With this question in mind, I'll discuss two conjectures (and supporting results) asserting that compact Riemannian manifolds with light behaving similarly to light in a compact locally symmetric space are necessarily isometric to a compact locally symmetric space.

Juan Souto

Kevin Wortman
A finitely-presented solvable group with a small quasi-isometry group
I'll present an example of an infinite, finitely-presented solvable group whose quasi-isometry group is a Lie group (over local fields).