[PAST EVENT] Mathematics Colloquium: Thomas Barthelmé (Queen's University)
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Mathematics Colloquium: Thomas Barthelmé (Queen's University)
Title: Anosov flow in higher dimensions
Abstract: Anosov flows and Anosov diffeomorphisms are the archetypical examples of a uniformly hyperbolic (a.k.a. chaotic) dynamical systems, and, as such, have been widely studied since their introduction by D. Anosov in the 60'.
An interesting problem in dynamics, or geometric topology, is to understand the link between a dynamical system and the topology of the manifolds that supports it. But despite all the work on Anosov flows the topology of manifolds that can support them is still very far from being well understood. In particular almost nothing is known when the dimension of the manifold is greater than 4, and one of the issues is the lack of examples.
In this talk, I will explain what Anosov flows are, some of the history of that field (including some claims that were made and turned out to be wrong) and how to build some examples in higher dimension. Some of the results mentioned in this talk are joint work with C. Bonatti, A. Gogolev and F. Rodriguez Hertz.