Spring 2012


April 16: Jim Tseng (UIUC)

Title: Dense and nondense orbits for pairs of maps

Abstract: For a pair of hyperbolic commuting linear maps of the torus, we show that the set of points dense under one map and nondense under the other is of full Hausdorff dimension. In dimension two, we can also show weaker results for noncommuting maps. Our technique for commuting maps can be applied to other spaces. This is joint work with V. Bergelson and M. Einsiedler.


April 30: Michele Lee (Michigan/Maryland)

Title: Dynamics on the PSL(2, C)-character variety of certain hyperbolic 3-manifolds

Abstract: The PSL(2, C)-character variety of a hyperbolic 3-manifold M is essentially the set of homomorphisms of the fundamental group of M into PSL(2, C), up to conjugacy. We will discuss the action of the group of outer automorphisms of the fundamental group of M on this space. In particular, we will discuss how one can find domains of discontinuity for the action.


May 25: Keith Burns (Northwestern)

Title: Conjugacy for geodesic flows in negative curvature

Abstract: It is believed that the geodesic flows for two compact Riemannian manifolds with negative curvature are conjugate by a homeomorphism that preserves time along orbits if and only the manifolds are isometric. The conjecture was proved for surfaces by Otal and in somewhat greater generality by Croke. I will discuss ideas that might or might not lead to a positive answer in higher dimensions.