Colloquium – Polona Durcik, California Institute of Technology
January 31 @ 11:00 am - 12:00 pm
Topic: On some singular Brascamp-Lieb inequalities
Abstract: Brascamp-Lieb inequalities are L^p estimates for certain multilinear integral forms on functions on Euclidean spaces. They generalize several classical inequalities, such as Hoelder’s inequality or Young’s convolution inequality. Brascamp-Lieb inequalities have been studied extensively in recent years. In this talk we focus on singular Brascamp-Lieb inequalities, which arise when one of the functions in a Brascamp-Lieb integral is replaced by a singular integral kernel. Singular Brascamp-Lieb integrals are much less understood than their non-singular variants. We give an overview of some results and open problems, and discuss applications to certain questions in Euclidean Ramsey theory.