NCGQG

Noncommutative geometry and quantum groups

Coordinatore	UNIVERSITETET I OSLO    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Norway [NO]
Totale costo	1˙144˙930 €
EC contributo	1˙144˙930 €
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-2012-StG_20111012
Funding Scheme	ERC-SG
Anno di inizio	2013
Periodo (anno-mese-giorno)	2013-01-01   -   2017-12-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITETET I OSLO  Organization address address: Problemveien 5-7 city: OSLO postcode: 313 contact info Titolo: Mr. Nome: Yngvar Cognome: Reichelt Email: send email Telefono: +47 228 57221	NO (OSLO)	hostInstitution	1˙144˙930.00
2	UNIVERSITETET I OSLO  Organization address address: Problemveien 5-7 city: OSLO postcode: 313 contact info Titolo: Prof. Nome: Sergiy Cognome: Neshveyev Email: send email Telefono: +47 228 55921	NO (OSLO)	hostInstitution	1˙144˙930.00

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 Obiettivo del progetto (Objective)

'The goal of the project is to make fundamental contributions to the study of quantum groups in the operator algebraic setting. Two main directions it aims to explore are noncommutative differential geometry and boundary theory of quantum random walks. The idea behind noncommutative geometry is to bring geometric insight to the study of noncommutative algebras and to analyze spaces which are beyond the reach via classical means. It has been particularly successful in the latter, for example, in the study of the spaces of leaves of foliations. Quantum groups supply plenty of examples of noncommutative algebras, but the question how they fit into noncommutative geometry remains complicated. A successful union of these two areas is important for testing ideas of noncommutative geometry and for its development in new directions. One of the main goals of the project is to use the momentum created by our recent work in the area in order to further expand the boundaries of our understanding. Specifically, we are going to study such problems as the local index formula, equivariance of Dirac operators with respect to the dual group action (with an eye towards the Baum-Connes conjecture for discrete quantum groups), construction of Dirac operators on quantum homogeneous spaces, structure of quantized C*-algebras of continuous functions, computation of dual cohomology of compact quantum groups. The boundary theory of quantum random walks was created around ten years ago. In the recent years there has been a lot of progress on the “measure-theoretic” side of the theory, while the questions largely remain open on the “topological” side. A significant progress in this area can have a great influence on understanding of quantum groups, construction of new examples and development of quantum probability. The main problems we are going to study are boundary convergence of quantum random walks and computation of Martin boundaries.'