Title:

Sphere packing and semidefinite programming

Abstract:

In this talk I will explain what semidefinite programming is and how it can be  used to compute bounds in extremal geometry. First I will focus on compact problems such as the spherical code problem, which asks for the largest number of points on a unit sphere such that the inner product between any pair of disctinct points is at most some given constant. Then I will discuss the (noncompact) sphere packing problem and related problems, and explain how semidefinite programming can be used to obtain improved bounds.