Archived Events

We introduce a new operation, double point surgery, on a configuration of surfaces in a 4-manifold, and use it to construct configurations that are smoothly knotted, without changing the topological type or the smooth embedding type of the individual components of the configuration. Taking branched covers, we produce smoothly exotic actions of $Z_m \oplus Z_n$ on simply connected 4-manifolds with complicated fixed-point sets.

The goal of this talk is to present results and examples about discrete subgroups of PU(2,1), which is the automorphism group of the complex hyperbolic plane. These groups are a complex 2-dimensional analogue of Fuchsian groups in PSL(2,R), or Kleinian groups in PSL(2,C). The complex hyperbolic space is an example of a rank one symmetric space with negative pinched curvature. It is biholomorphic to a ball, and is a natural generalisation of the usual Poincaré disk or upper half plane.

Asymptotically hyperbolic manifolds are a natural generalization of infinite volume hyperbolic manifolds and enjoy similar features.  In this talk, we'll recall the definition of these spaces and see some examples.  After a brief discussion of their spectral theory and dynamics, I will present a prime orbit theorem and a "dynamical wave trace formula."  Based on the prime orbit theorem and the trace formula, we will determine a relationship between the existence of pure point spectrum and the topological entropy of the geodesic flow.  We can interpret th