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Points on spheres and their orthogonal lattices

Presented by: 
M Aka EPFL - Ecole Polytechnique Fédérale de Lausanne
Date: 
Monday 9th June 2014 - 14:30 to 15:30
Venue: 
INI Seminar Room 2
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.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons