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).