Groups and Dynamics Seminar

Date: February 15, 2023

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Yury Kudryashov, Texas A&M University

Title: 4-periodic orbits in planar billiards

Abstract: Let Ω be a domain in a Euclidean space of dimension d≥2 with sufficiently smooth boundary. Consider the corresponding billiard: a particle moves along straight lines inside Ω and reflects against the boundary of Ω by the standard reflection law. In 1978, Victor Ivrii conjectured that almost every trajectory of this billiard is non-periodic. This condition appeared as a natural geometric assumption in his theorem about asymptotic behavior of the spectrum of the Dirichlet problem for the Laplace operator in Ω. When this conjecture was formulated, people from Sinai's seminar in Moscow predicted it to be solve in a couple of weeks. More than 40 years later, the conjecture still stands.