Talk by Dr. Anja Randecker (Department of Mathematics, University of Toronto)

4/10/2019  Wilson Hall 1-144  4:10-5:00pm


Translation surfaces arise naturally in many different contexts such as the theory of mathematical billiards, of Teichmüller spaces, or of holomorphic differentials. They can be described by finitely many polygons that are glued along edges which are parallel and have the same length. In recent years, people have asked what happens when we glue infinitely instead of finitely many polygons. From that question the field of infinite translation surfaces has evolved.

In my talk, I will introduce finite and infinite translation surfaces and explain one example of a recent result that bridges between these two concepts: With Howard Masur and Kasra Rafi, we studied the average diameter of translation surfaces of a given type. We prove that asymptotically, the average diameter of translation surfaces of genus g and area 1 goes to 0 when g goes to infinity.