The geometry of singular integral operators

Abstract

Singular integral operators are among the most classical objects of study in harmonic analysis, arising naturally in complex analysis and partial differential equations. Originally studied on the line and smooth curves, in the last 50 years a rich theory of singular integrals on rough sets has been developed. This talk will be a gentle introduction to the topic, and our motivating question will be the classical Painlevé problem: what is the geometry of removable singularities for bounded holomorphic functions?

Damian Dąbrowski

Assistant professor

My research interests include geometric measure theory and harmonic analysis.