Stefan Steinerberger, Yale University, Universal limitations of quadrature rules and generalized spherical designs
Sprache des Titels:
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.