Stephanie Vance: Sphere Packings in Euclidean Space (C-401)

Current Topics Seminar

Speaker	Stephanie Vance
Title	Sphere Packings in Euclidean Space (C-401)
Date	January 20 4:00pm PDL C-36

The classical sphere packing problem asks: how densely can one pack identical balls into R^n so that the ball interiors do not overlap? Besides being a natural geometric question to ask, this problem is relevant to both number theory and digital communications. In this talk I will introduce the sphere packing problem, review its history, and survey some of the known results. I will then focus on sphere packings that have interesting algebraic structures and explain how they can be used to obtain new lower bounds for the optimal sphere packing density in high dimensions divisible by four. Note: this talk will be held on a Tuesday in C-401.