Integrable Billiards and Rigidity - Lecture 1

Explore the recent advancements in the Birkhoff-Poritsky conjecture for convex billiards in the plane during this CRM Nirenberg Lecture in Geometric Analysis. Delve into Misha Bialy's approach to the conjecture, which is rooted in E. Hopf type rigidity from Riemannian geometry. Gain insights into the original Hopf method and its extension to Twist symplectic maps and billiards. Examine a criterion for local maximality of billiard orbits using Jacobi fields. Learn about the conjecture that posits ellipses as the only integrable convex billiards and the progress made in this area of mathematical research.