Olga Bernardi (University of Padova)
Symplectic billiards were introduced by P. Albers and S. Tabachnikov in 2018 as a simple dynamical system where, opposed to Birkhoff billiards, the generating function is the area instead of the length. We first recall the main properties of symplectic billiards in strictly-convex domains. We proceed by presenting
this recent result: if the phase-space is fully foliated by continuous invariant curves which are not null-homotopic, then the boundary of the billiard table is an ellipse.
We finally discuss the state of the art
both of integrability and of area spectral rigidity for these billiards.
Joint works with Luca Baracco and Alessandra Nardi.