The MathNet Korea
Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

고려대학교 수학과 세미나
Title Effective equidistributio​n of rational points on certain expanding horospheres
Date 2019-01-07
Speaker 이민(University of Bristol)
Sponsors 2019-01-07
Host KOREA Univeristy
Place 아산이학관 526호
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 equidistributio​n of 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-classif​ication 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 extends my work with J. Marklof, on the 3-dimensional case (2017). This is a joint work with D. El-Baz and B. Huang.