Vadim Kaloshin, University of Maryland
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 obstacles.