Distributing points on the sphere

Dmitriy Bilyk
UMN
Friday, September 15, 2017 -
2:30pm to 3:30pm
Vincent Hall 206

Many mathematical problems require constructing well-distributed sets
of points on the sphere. The quality of such distributions can be
measured in a variety of analytic and geometric ways: energy
minimization, covering/packing radii, discrepancy, tessellations,
isometric embeddings etc. Different random, semi-random, and
deterministic constructions are known, although in general the problem
remains quite difficult. We shall survey some of the ideas and discuss
recent results (joint with M. Lacey) on uniform tessellations of the
sphere by hyperplanes and almost isometric embedding of subsets of the
sphere into the Hamming cube, which are in turn related to one-bit
compressed sensing.