Edmond Koudjinan (IST Austria):

Title: On the Birkhoff conjecture for nearly centrally symmetric domains

Abstract: In this talk, I will discuss a recent advance on Birkhoff conjecture, namely a proof that : an integrable, nearly centrally symmetric Birkhoff billiard table is necessarily an ellipse. This is done by combining recent breakthroughs by Bialy-Mironov (who prove the conjecture for centrally symmetric Birkhoff billiard tables) and by Kaloshin-Sorrentino (who prove the conjecture for Birkhoff billiard tables close to ellipses). In particular, we shall discuss the use of nonstandard generating functions discovered by Bialy-Mironov. This is a joint work with Ke Zhang and V. Kaloshin.