A Survey Lecture on Billiards

Explore the fascinating world of mathematical billiards in this engaging 44-minute survey lecture presented by Richard Evan Schwartz for the International Mathematical Union. Delve into the intriguing properties of billiard trajectories, discover the connections between billiards and various areas of mathematics, and gain insights into the latest research developments in this field. Learn about periodic orbits, ergodicity, and the role of symmetry in billiard systems. Examine different types of billiard tables, including polygonal and elliptical shapes, and understand how their geometry affects the behavior of billiard balls. Investigate open problems and current areas of active research in mathematical billiards, providing a comprehensive overview of this captivating subject for mathematicians and enthusiasts alike.