Sala Conferenze (Puteano, Centro De Giorgi).
In 1927 G. Birkhoff conjectured that if a billiard in a strictly convex smoothdomain is integrable, the domain has to be an ellipse (or a circle). Theconjecture is still wide open, and presents remarkable relations with openquestions in inverse spectral theory and spectral rigidity. In the talk we show that a version of Birkhoff’s conjecture is true for smallperturbations of ellipses of small eccentricity. This is joint work with A. Avila and V. Kaloshin