February 9, 2017

Discrepancy and Energy Optimization (On the Sphere)

There are many different ways to measure how well a discrete set is distributed in a given domain, in particular, on the sphere: discrepancy and discrete energy are among the most popular ones. In various situations these two objects turn out to be intricately related to each other. In recent work, we have found several new manifestations and generalizations of this phenomenon with some surprising consequences in energy optimization. We shall present a non-technical survey of  old and recent results and interactions between these areas,  as well as connections  to problems in  other fields: combinatorial geometry, one-bit-compressed sensing, embeddings of metric spaces, etc. Tea at 3:30 pm in SC 1425. (Contact Person: Ed Saff)