Sino-Russian Mathematics Center-JLU Colloquium (2025-005)—Integrable Birkhoff billiards inside cones

Title: Integrable Birkhoff Billiards inside Cones
Speaker: Andrey Mironov
Institution: Sobolev Institute of Mathematics
Date & Time: February 21, 2025, 10:30–12:30
Location: Seminar Room 5, Mathematics Building, Jilin University

The classical Birkhoff conjecture posits that if planar billiards within a closed smooth convex curve are integrable, then the curve must be an ellipse. In higher dimensions, all known integrable billiards are confined to tables composed of quadric segments. This study investigates Birkhoff billiards within convex cones in ${\mathbb{R}}^n$ and proves that billiards in any $C^3$-smooth convex cone are integrable. These findings provide the first examples of integrable billiard tables in ${\mathbb{R}}^n$ that are not associated with quadrics.

Professor Andrey Mironov serves as the acting director of the Sobolev Institute of Mathematics and is a Corresponding Member of the Russian Academy of Sciences. His research interests encompass Integrable Systems, Geometry, Mathematical Physics, and Dynamical Systems.