Dynamical Systems: the Mathematics of Billiards

Undergraduate / Graduate

We will begin by introducing the subject of billiards in polygons, using billiards then as a motivation to study some basic notions in the field of dynamical systems. We will then apply these ideas to billiards. We will then introduce a special class of rational angled billiards and show how they lead to the subject of translation surfaces. We then will study properties of translation surfaces and study families of them which are called moduli spaces.