Rice University Department of Mathematics Colloquium

Dynamics and geometry on surfaces

4:00 pm Thursday, March 2nd, 2017
Simion Filip (Harvard University)

Abstract: Dynamics in one or two dimensions is tightly related to the geometry of surfaces. For example, billiards in polygons and interval exchange transformations lead naturally to Riemann surfaces with flat metrics and cone-angle singularities. The investigation of the corresponding moduli spaces began in the work of Veech and is currently a very active area of research. After surveying some of the recent developments in the area, I will discuss extensions to higher dimensions, based on the geometry of K3 surfaces. These are complex 2-dimensional (so real 4-dimensional) manifolds, with a rich geometry and admitting interesting dynamical systems. Part of the work is joint and in progress with Phil Engel; I will provide the necessary back ground and motivation.

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