Points on spheres and their orthogonal lattices
Seminar Room 2, Newton Institute Gatehouse
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.
This talk has not been recorded because the speaker withheld their permission.