Abstract: When playing billiards, we have a domain Q - the billiard table - and consider the motion of a particle that travels uniformly within Q, and bounces off elastically - angle of reflection equals
angle of incidence - when reaching the boundary of Q. The characteristic features of this motion can be quite different depending on the shape of the domain: this is a playground where mathematicians can find toys according to their tastes. On the other hand, billiards naturally arise as models in statistical physics: several interesting phenomena can be formulated, and possibly treated in a rigorous manner by means of these systems. In my talk I would like to
describe these two aspects of billiards, mentioning briefly some challenges that the theory faces currently.
You can watch the lecture here: