Third Year Major Oral: Entangled Singular Integral Operators

Abstract: 

In this talk, we will explore some modern research directions related to singular integral operators (SIOs).

In particular, we focus on SIOs beyond the classical one-parameter and multi-parameter settings. These SIOs include those that are invariant with respect to the so-called entangled dilations, the main example being the case of Zygmund dilations. They also include the Flag SIOs -- certain particular multi-parameter SIOs -- the theory of which shares some common difficulties with the Zygmund dilation case.

Our main focus is on commutator estimates in the above mentioned settings. We discuss recent work and open questions regarding commutators, highlighting challenges and potential directions for future research. These include iterated commutators and mixed-norm questions.