Periodic billiard paths on regular polygons- Diana Davis (Swarthmore College)
Abstract: Mathematicians have understood periodic billiards on the square for hundreds of years, and my collaborator Samuel Lelièvre and I have understood them on the regular pentagon for about five years now. During the COVID-19 pandemic, I have been in France, working with Samuel to extend our understanding to all regular polygons with an odd number of sides. In this talk, I'll briefly explain results and techniques for the square and pentagon, and then show lots of nice pictures of billiards on polygons with more than 5 sides, that we have created recently.
An invitation to dilation surfaces- Selim Ghazouani (University of Warwick)
Abstract: In this video talk, I will introduce dilation surfaces, their moduli spaces and related foliations on surfaces and then try to give some motivation for a range of open problems.
You can “hear” the shape of a polygonal billiard table- Chandrika Sadanand (University of Illinois Urbana Champaign)
Abstract: Consider a polygon-shaped billiard table on which a ball can roll along straight lines and reflect off of edges infinitely. In work joint with Moon Duchin, Viveka Erlandsson and Chris Leininger, we have characterized the relationship between the shape of a polygonal billiard table and the set of possible infinite edge-itineraries of balls travelling on it. In this talk, we will explore this relationship and the tools used in our characterization (notably a new rigidity result for flat cone metrics).