EVENT DETAILS AND ABSTRACT

Title: On the Integral Geometry of Liouville Billiard Tables
Speaker: Petar Topalov
Speaker Info: Northeastern
Brief Description:
Special Note:
Abstract:

The notion of a Radon transform is introduced for completely integrable billiard tables. In the case of Liouville billiard tables of dimension $3$ we prove that the Radon transform is one-to-one on the space of continuous functions $K$ on the boundary which are invariant with respect to the corresponding group of symmetries. We prove also that the frequency map associated with a class of Liouville billiard tables is non-degenerate. This allows us to obtain spectral rigidity of the corresponding Laplace-Beltrami operator with Robin boundary conditions.