NCDFP

Non-Commutative Distributions in Free Probability

Coordinatore	UNIVERSITAET DES SAARLANDES    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Germany [DE]
Totale costo	2˙197˙000 €
EC contributo	2˙197˙000 €
Programma	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)
Code Call	ERC-2013-ADG
Funding Scheme	ERC-AG
Anno di inizio	2014
Periodo (anno-mese-giorno)	2014-02-01   -   2019-01-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITAET DES SAARLANDES  Organization address address: CAMPUS city: SAARBRUECKEN postcode: 66041 contact info Titolo: Ms. Nome: Corinna Cognome: Hahn Email: send email Telefono: +49 681 95923362 Fax: +49 681 95923370	DE (SAARBRUECKEN)	hostInstitution	2˙197˙000.00
2	UNIVERSITAET DES SAARLANDES  Organization address address: CAMPUS city: SAARBRUECKEN postcode: 66041 contact info Titolo: Prof. Nome: Roland Cognome: Speicher Email: send email Telefono: +49 681 302 2427 Fax: +49 681 302 2476	DE (SAARBRUECKEN)	hostInstitution	2˙197˙000.00

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 Obiettivo del progetto (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'