UBC HAFG 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 a classical Fourier-analytic approach. Afterwards, following a recent joint work with Ravotti, we take up the same question in the hyperbolic plane, focusing however on its upgrade to the unit tangent bundle. This allows abstract harmonic analysis to enter the picture, in the form of the theory of unitary representations of the special linear group. In conjunction with an ingenious strategy pioneered by Ratner in the eighties, the method leads to a full quantitative understanding of the uniform distribution properties of expanding dilates of homogeneous curves on compact hyperbolic surfaces, thereby refining the qualitative analogue established by Margulis in his doctoral thesis.