Speaker：Shucheng Yu (University of Science and Technology of China)

Time：2024-12-7, 14:00

Location：Conference Room S106 at Experiment Building at Haiyun Campus

Abstract:

Given a planar point set with a constant density, one can study the limiting distribution of gaps for directions (i.e. projection to the unit sphere) of points from this point set in larger and larger disks. For primitive integer points an explicit formula for the limiting gap distribution function was obtained by Boca, Cobeli, and Zaharescu using analytic number theory. This formula was later extended by Marklof and Strömbergsson for any lattices using homogeneous dynamics. More recently, they showed the limiting gap distribution function exists for point sets of cut-and-project type. The main theme of the dynamical approach is that the limiting gap distribution function is expressed in terms of the measure of certain sets in the corresponding homogeneous space. In this talk I will describe a tail asymptotic formula for the limiting gap distribution functions from this point of view. This is joint work with Gustav Hammarhjelm and Andreas Strömbergsson.