Edmond Koudjinan (Institute of Science and Technology, Austria):

Title:
On non co-existence of $2$-- and $2m+1$-- rational caustics.

Abstract: 
In this talk, I will discuss recent results concerning the question of co-existence of two rational caustics by nearly circular billiard tables. In particular, I will give a partial answer to a conjecture by Tabachnikov. This is based on a joint work with Vadim Kaloshin.