Multiparameter Dyadic Harmonic Analysis and Probabilistic Methods

The project "Multiparameter Dyadic Harmonic Analysis and Probabilistic Methods" studied singular integral operators in the linear and multiparameter (or product) settings. This was a three-year postdoctoral project of mathematics at the University of Helsinki with research periods at the Georgia Institute of Technology and CRM. The key feature of singular integrals is cancellation between negative and positive values. It is not enough to study their size, since the cancellation has to be captured in a delicate way. The project developed new theorems and methods to study the boundedness of singular integrals in complicated situations. This led to multiple publications in leading scientific journals (e.g. Annales scientifiques de l'École normale supérieure). The project also contributed significantly to problems related to geometry. The connection to singular integrals is explained by the theory of uniform rectifiability developed by David and Semmes.