Lecture
This lecture by the instructor covers the properties of curves with Poritsky property and Liouville nets in billiards. It discusses caustics, Birkhoff integrability, Graves property, and the relationship between Poritsky and Liouville properties. The lecture also explores the conservation laws for billiard actions, the string construction method, and the concept of Liouville nets. Various theorems and results related to billiards on constant curvature surfaces are presented, along with examples and applications in the general Riemannian context.