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Research

Dynamical Systems Seminar

Integrability and rigidity for convex billiard (1-5)

Speaker: Vadim Kaloshin (Institute of Science and Technology Austria)
Time: Jun 8, 2022, 17:00-18:00
Location: Zoom ID 814 8838 2531

Time: 17:00-18:00, June 8,10, 13, 14 and 15, 2022

Abstract

During the five talks I will discuss billiards inside of a convex planar domain, called Birkhoff billiards. Dynamics of Birkhoff billiards is closely connected to a classical question, popularized by M. Kac: "Can you hear the shape of a drum?"

A convex planar domain gives rise to two spectra: the Laplace spectra, via the Dirichlet boundary value problem, and the length spectra as the set of length of all billiard periodic orbits. These two spectra are closely related. One interesting particular case of the Kac question is so-called spectral rigidity asking if there is a deformation keeping one of the spectra fixed. We shall discuss recent progress on this problem.