Polygonal billiards, flat surfaces, and translation flows: to infinity and beyond

The study of translation flows on flat surfaces falls in the broad field of Teichmüller dynamics, which is the meeting point of many fields: ergodic theory, algebraic geometry, combinatorics, number theory, etc. Its aim is to study generalizations of linear flows on two-dimensional tori. In this talk, I will survey the origins of the field, state some classical results, and mention some recent efforts to develop the theory further to include surfaces of infinite type. No previous background in the field will be assumed.