Noncommutative Calderón-Zygmund theory, operator space geometry and quantum probability

Objectif

Von Neumann's concept of quantization goes back to the foundations of quantum mechanics
and provides a noncommutative model of integration. Over the years, von Neumann algebras
have shown a profound structure and set the right framework for quantizing portions of algebra,
analysis, geometry and probability. A fundamental part of my research is devoted to develop a
very much expected Calderón-Zygmund theory for von Neumann algebras. The lack of natural
metrics partly justifies this long standing gap in the theory. Key new ingredients come from
recent results on noncommutative martingale inequalities, operator space theory and quantum
probability. This is an ambitious research project and applications include new estimates for
noncommutative Riesz transforms, Fourier and Schur multipliers on arbitrary discrete groups
or noncommutative ergodic theorems. Other related objectives of this project include Rubio
de Francia's conjecture on the almost everywhere convergence of Fourier series for matrix
valued functions or a formulation of Fefferman-Stein's maximal inequality for noncommutative
martingales. Reciprocally, I will also apply new techniques from quantum probability in
noncommutative Lp embedding theory and the local theory of operator spaces. I have already
obtained major results in this field, which might be useful towards a noncommutative form of
weighted harmonic analysis and new challenging results on quantum information theory.

Champ scientifique

Régime de financement

ERC-SG - ERC Starting Grant

Institution d’accueil

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS

Contribution de l’UE

€ 1 090 925,00

Adresse

CALLE SERRANO 117
28006 Madrid
Espagne

Région

Comunidad de Madrid Comunidad de Madrid Madrid

Type d’activité

Research Organisations

Contact administratif

Ana Maria De La Fuente (Ms.)

Chercheur principal

Javier Parcet Hernandez (Dr.)

Liens

Contacter l’organisation Site web

Coût total

Aucune donnée

Bénéficiaires (1)