Lectures & Talks
2019 Fall POSTECH PMI Number Theory Seminar
Place: 404 Math building
Title : Effective equidistribution of rational points on expanding horospheres
Abstract : The main purpose of this talk is to provide an effective version of a result due to Einsiedler, Mozes, Shah and Shapira, on the equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in at least 3 dimensions. Their proof uses techniques from homogeneous dynamics and relies in particular on measure-classification theorems due to Ratner. Instead, we pursue an alternative strategy based on spectral theory, Fourier analysis and Weil’s bound for Kloosterman sums
which yields an effective estimate on the rate of convergence in the space of (d+1)-dimensional Euclidean lattices with d>1.
This is a joint work with D. El-Baz and B. Huang, extending my work with J. Marklof on the 3-dimensional case.