Objetivo Von Neumann's concept of quantization goes back to the foundations of quantum mechanicsand provides a noncommutative model of integration. Over the years, von Neumann algebrashave 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 avery much expected Calderón-Zygmund theory for von Neumann algebras. The lack of naturalmetrics partly justifies this long standing gap in the theory. Key new ingredients come fromrecent results on noncommutative martingale inequalities, operator space theory and quantumprobability. This is an ambitious research project and applications include new estimates fornoncommutative Riesz transforms, Fourier and Schur multipliers on arbitrary discrete groupsor noncommutative ergodic theorems. Other related objectives of this project include Rubiode Francia's conjecture on the almost everywhere convergence of Fourier series for matrixvalued functions or a formulation of Fefferman-Stein's maximal inequality for noncommutativemartingales. Reciprocally, I will also apply new techniques from quantum probability innoncommutative Lp embedding theory and the local theory of operator spaces. I have alreadyobtained major results in this field, which might be useful towards a noncommutative form ofweighted harmonic analysis and new challenging results on quantum information theory. Ámbito científico natural sciencesphysical sciencesquantum physicsnatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsgeometry Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2010-StG_20091028 Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS Aportación de la UE € 1 090 925,00 Dirección CALLE SERRANO 117 28006 Madrid España Ver en el mapa Región Comunidad de Madrid Comunidad de Madrid Madrid Tipo de actividad Research Organisations Contacto administrativo Ana Maria De La Fuente (Ms.) Investigador principal Javier Parcet Hernandez (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS España Aportación de la UE € 1 090 925,00 Dirección CALLE SERRANO 117 28006 Madrid Ver en el mapa Región Comunidad de Madrid Comunidad de Madrid Madrid Tipo de actividad Research Organisations Contacto administrativo Ana Maria De La Fuente (Ms.) Investigador principal Javier Parcet Hernandez (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos