Stefan Steinerberger, Yale University, Universal limitations of quadrature rules and generalized spherical designs

Description

How many points does one have to place on a sphere so that the average of every polynomial up to degree k on the sphere coincides with the average on these points? These spherical designs have been introduced in the 70s and studied intensively ever since - a recent paper of Bondarenko, Radchenko \& Viazovska (Annals 2013) concludes the theory. We give a vast generalization to general compact manifolds and to weighted averages. The techniques are completely new and based on partial differential equations, the results are new even on $S^2$. If time allows, I will discuss a generalized Sturm Oscillation theorem that is based on similar ideas.

Period	29 Dec 2017
Event type	Guest talk
Location	AustriaShow on map