UBC Ergodic Theory Seminar: Emilio Corso

What happens to a progressively dilating body when folding the space in which it lives? For a start, we shall examine the problem in a Euclidean context, surveying results of Randol and Strichartz through the quantitative, fractal-geometric viewpoint of Fourier dimension. Afterwards, we take up the same question in hyperbolic spaces, briefly overviewing the equidistribution theorems of Randol and Sarnak while focusing instead on their upgrade to unit tangent bundles, due originally to Margulis and later refined quantitatively in our joint work with Ravotti. If time permits, we present applications of the latter result to closely related probabilistic and number-theoretic questions.