The APDE seminar on Monday, 8/29, will be given by Vadim Kaloshin (ISTA) both in-person (in 740 Evans) and online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (firstname.lastname@example.org).
Title: Marked Length Spectral determination of analytic chaotic billiards
Abstract: We consider billiards obtained by removing from the plane three strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides natural labeling of periodic orbits. Jointly with J. De Simoi and M. Leguil we show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of all obstacles. For obstacles without symmetry assumption, V. Otto recently showed that the Marked Length Spectrum along with information about two obstacles determines the geometry of all remaining obstacle.