Combinatorics Seminar
When: Sunday, December 16, 10am
Where: Schreiber 309
Speaker: Ilya Dumer, University of California at Riverside
Title: Covering a sphere with unit spheres: Rogers bound
revisited
Abstract:
Given a sphere of any radius in an n-dimensional Euclidean space,
we study the coverings of this sphere with unit spheres of radius 1.
Our goal is to obtain the lowest covering density, which is
the average number of unit spheres needed to cover a point in
a bigger sphere. For a growing dimension n, we design a covering with
an asymptotic density (n ln n)/2. The techniques combine random-coding
arguments with a new "porous" covering design and geometric estimates.
This new bound gives the lowest covering density known to date and
is half the order n ln n established in the classical Rogers bound
of 1956.