Rice University Department of Mathematics Colloquium
Closed curves on surfaces
4:00 pm Thursday, September 22th, 2016
Francis Bonahon (USC)
Abstract: The title of the talk should be “What I learned during my last visit to Rice, in 1985”. At that time, I was using ideas from dynamical systems to study a very topological topic: closed curves on surfaces, considered up to homotopy. The conversations I had with Bill Veech at Rice led me to reverse the process, and to use ideas from topology to study geometric properties of hyperbolic metrics on surfaces. The connection involves transverse measures for the geodesic flow of the surface, and the interpretation of a hyperbolic metric as a “random closed curve”. I will discuss what came out of these ideas, including recent developments.
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