Seminar

Given a topology S, how many ways (if any) are there of putting some kind of classical geometry on S? For example, the sphere has no compatible system of coordinates with Euclidean geometry. (There is no metrically accurate atlas of the world.) On the other hand, the 2-torus admits a rich supply of Euclidean structures, which form an interesting moduli space which itself enjoys hyperbolic non-Euclidean geometry. For other geometric structures, the moduli spaces are much more complicated and are best described by a dynamical system. This talk will survey some of the interesting dynamical systems which arise for simple examples of geometries on surfaces.