Skip to content

GAN

Seminar

Points on spheres and their orthogonal lattices

Aka, M (EPFL - Ecole Polytechnique Fédérale de Lausanne)
Monday 09 June 2014, 14:30-15:30

Seminar Room 2, Newton Institute Gatehouse

Abstract

It is a classical question to understand the distribution (when projected to the unit sphere) of the solutions of x^2+y^2+z^2=D as D grows. To each such solution v we further attach the lattice obtained by intersecting the hyperplane orthogonal to v with the set of integral vectors. This way, we obtain, for any D that can be written as a sum of three squares, a finite set of pairs consisting of a point on the unit sphere and a lattice. In the talk I will discuss a joint work with Manfred Einsiedler and Uri Shapira which considers the joint distribution of these pairs in the appropriate spaces. I will outline a general approach to such problems and discuss dynamical input needed to establish that these pairs distribute uniformly.

Video

This talk has not been recorded because the speaker withheld their permission.

Back to top ∧