Objective This research project focuses on the structure, classification and rigidity of three closely related objects: group actions on measure spaces, orbit equivalence relations and von Neumann algebras. Over the last 15 years, the study of interactions between these three topics has led to a process of mutual enrichment, providing both striking theorems and outstanding conjectures.Some fundamental questions such as Connes' rigidity conjecture, the structure of von Neumann algebras associated with higher rank lattices, or the fine classification of factors of type III still remain untouched. The general aim of the project is to tackle these problems and other related questions by developing a further analysis and understanding of the interplay between von Neumann algebra theory on the one hand, as well as ergodic and group theory on the other hand. To do so, I will use and combine several tools and develop new ones arising from Popa's Deformation/Rigidity theory, Lie group theory (lattices, boundaries), topological and geometric group theory and representation group theory (amenability, property (T)). More specifically, the main directions of my research project are:1) The structure of the von Neumann algebras arising from Voiculescu's Free Probability theory: Shlyakhtenko's free Araki-Woods factors, amalgamated free product von Neumann algebras and the free group factors.2) The structure and the classification of the von Neumann algebras and the measured equivalence relations arising from lattices in higher rank semisimple connected Lie groups.3) The measure equivalence rigidity of the Baumslag-Solitar groups and several other classes of discrete groups acting on trees. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebranatural sciencesmathematicsapplied mathematicsstatistics and probabilitynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-StG-2014 - ERC Starting Grant Call for proposal ERC-2014-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution UNIVERSITE PARIS-SACLAY Net EU contribution € 844 473,75 Address BATIMENT BREGUET - 3 RUE JOLIOT CURIE 91190 Gif-Sur-Yvette France See on map Region Ile-de-France Ile-de-France Essonne Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 844 473,75 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all UNIVERSITE PARIS-SACLAY France Net EU contribution € 844 473,75 Address BATIMENT BREGUET - 3 RUE JOLIOT CURIE 91190 Gif-Sur-Yvette See on map Region Ile-de-France Ile-de-France Essonne Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 844 473,75 CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Participation ended France Net EU contribution € 32 276,25 Address RUE MICHEL ANGE 3 75794 Paris See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 32 276,25
