UBC Probability Seminar: Emilio Corso

A momentous legacy of twentieth-century mathematics is the realisation that deterministically evolving systems frequently exhibit, when observed for sufficiently extended periods of time, a statistical behaviour akin to the limiting behaviour of independent random variables. We shall explore a geometric incarnation of this surprising phenomenon, overviewing various kinds of statistical limit theorems for the free motion of a particle on a negatively curved surface. In order to emphasise the richness of possible asymptotic behaviours, as well as the variety of sources of randomness, we will further compare the free-motion dynamics with a closely related evolution on the same phase space, known as the horocycle flow.