Richard Schwartz (Brown University) : Pappus's Theorem, the Modular Group, and Patterns of Geodesics

Following up on work I did in my youth, I will discuss how the iteration of Pappus's Theorem is connected to what are now called relatively Anosov representations of the modular group in the Barbot component.  (Back in the day they didn't have a name, and for the talk you don't need to know anything about Anosov representations to understand them.)  I will also explain how the construction leads to patterns of geodesics in the symmetric space X=SL_3(R)/SO(3) that have the asymptotic properties coming from the Farey tesselation of the hyperbolic plane.   Finally, I will show a really nice computer program that I have been working on recently, which illustrates some of the constructions.