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Noncommutative analysis on groups and quantum groups

par Dupré Emilie - publié le , mis à jour le

Period : January 2020 - Juin 2024.

Description : This project deals with noncommutative (abbreviated to NC) analysis of topics related to multipliers. NC analysis is a new research direction emerging from operator spaces, quantum probability and NC harmonic analysis.

Fourier and Schur multipliers are at the intersection of these areas and play a key role in recent research motivated by concepts and problems from operator algebras and geometric group theory. They are natural examples of maps on NC Lp-spaces and intimately linked with NC functional inequalities. They are also used to formulate geometric properties (weak amenability, Haagerup property) of groups and quantum groups in terms of von Neumann algebras. Interactions between different approaches at the frontiers of NC analysis have given impressive discoveries. Our project will allow to open a vast avenue of perspectives and to reach a new level of development in these competitive fields by joining competences in combinatorics, geometric group theory and operator spaces.

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