Weakly mixing billiards in polygons 

Speaker. Giovanni Forni
Date. 06.06.23 at 2:00 pm

Abstract. According to numerical simulations (Artuso,Casati, Guarneri,  Prosen, Wang, …) the billiard in the random polygon is ergodic and mixing. The mathematical theory of billiards in polygons is rather well-developed for billiards in *rational* polygons (with limitations that will be explained), but there are few results on the ergodic theory of *typical* polygons. 
Kerchoff-Masur-Smillie proved in 1986 that ergodic polygons are dense (in the space of polygons), by fast approximation based on their ergodicity result for rational polygons. In this talk we will present a joint result with Jon Chaika that weakly mixing polygons are also dense.