Objective "We intend to study new directions in free probability theory with high potential to lead to breakthroughs in our understanding of random matrix models and operator algebras. We will drive forward the study of ""free analysis"" which is intended to provide a whole new mathematical theory for variables with the highest degree of non-commutativity and which lies at the crossroad of many exciting mathematical subjects.More specifically, the objective of the proposal is to extend our armory for dealing with non-commutative distributions and to attack some of the fundamental problems which are related to such distributions, like: the existence and properties of the limit of multi-matrix models; the isomorphism problem for free group factors, and more generally, properties of free entropy and free entropy dimension as invariants for von Neumann algebras.The main directions are:(i) classifying non-commutative symmetries and describing the effect of invariance under such quantum symmetries for non-commutative distributions; this will rely on our recent theory of easy quantum groups(ii) proving regularity properties for non-commutative distributions; for this we will develop the theory of free Malliavin calculus(iii) providing algorithms for calculating non-commutative distributions; this will rely on advances of the analytic theory of operator valued free convolutions and will in particular lead to a master algorithm for the computation of asymptotic eigenvalue distributions for general random matrix problems" Fields of science natural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebranatural sciencesmathematicsapplied mathematicsstatistics and probability Programme(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) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2013-ADG See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution UNIVERSITAT DES SAARLANDES EU contribution € 2 197 000,00 Address CAMPUS 66123 Saarbrucken Germany See on map Region Saarland Saarland Regionalverband Saarbrücken Activity type Higher or Secondary Education Establishments Principal investigator Roland Speicher (Prof.) Administrative Contact Corinna Hahn (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITAT DES SAARLANDES Germany EU contribution € 2 197 000,00 Address CAMPUS 66123 Saarbrucken See on map Region Saarland Saarland Regionalverband Saarbrücken Activity type Higher or Secondary Education Establishments Principal investigator Roland Speicher (Prof.) Administrative Contact Corinna Hahn (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
