Abstract: On Tuesday, we used abelianization to get a look at the distinctive Poisson geometry of the Teichmüller space of a punctured surface. Today, we’ll try to do the same on a compact surface. In this setting, however, the abelianization machine encounters severe technical difficulties. I’ll get it unstuck using tools from an unexpected source: the dynamical theory of billiards. Our venture into dynamics will be rewarded with a glimpse of exotic wall-crossing behavior not seen in the punctured surface case.

http://arxiv.org/abs/1510.05757