Schur multipliers, rigidity and noncommutative Harmonic Analysis

Objective

The proposal Schur-Rigidity NCHA (Schur multipliers, rigidity and noncommutative Harmonic Analysis) deals with questions in pure mathematics at the intersection of harmonic analysis, operator algebras and group theory. Its aim is provide the applicant Eduardo Tablate with the perfect environment to make a significant impact in these latter two fields, which are well-represented in Lyon, using his recognized expertise in classical harmonic analysis. The objectives involve more precisely investigations on boundedness properties of Schur multipliers, parallel to boundedness of Fourier multipliers in classical harmonic analysis, and with applications to the structure of group von Neumann algebras, their non-commutative Lp spaces. A focus will be made on semisimple groups and their lattices and also on free groups. Another objective is to explore further aspects of non-commutative Calderon-Zygmund theory. The common inspiration for these projects is the understanding that advanced harmonic analysis techniques can be effectively adapted in such a non-commutative settings and have a significative impact.