Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, November 24, 2014

Schreiber 006, 12:15

Zeev Rudnick

Tel Aviv University

Sums of three squares and spatial statistics on the sphere

A celebrated result of Legendre and Gauss determines which integers can be represented as a sum of three squares, and for those it is typically the case that there are many ways of doing so. These different representations give collections of points on the unit sphere, and a fundamental result, conjectured by Linnik, is that under a simple condition these become uniformly distributed on the sphere. In the lecture I will explore what happens beyond uniform distribution, giving evidence to randomness on smaller scales, examining quantities such as the electrostatic potential and nearest neighbour statistics. (joint work with J. Bourgain and P. Sarnak).

Coffee will be served at 12:00 before the lecture
at Schreiber building 006