Anja Randecker

Saddle connection complex: coarse and fine

Translation surfaces arise naturally in many different contexts such as the theory of Teichmüller spaces, of mathematical billiards, or of stability conditions of categories. A new approach to study translation surfaces is to encode their geometry in a combinatorial object, called the saddle connection complex. For translation surfaces, this complex plays the same role as its more established cousin, the arc complex, does for topological surfaces.

In this talk, I will introduce the saddle connection complex and some properties of its fine geometry (in particular Ivanov-type rigidity) and its coarse geometry (in particular no quasi-isometric rigidity). Both is based on joint works with Valentina Disarlo, Huiping Pan, and Robert Tang.