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Noncommutative Geometry

Noncommutative Geometry

Objective

European scientists have played leading roles in many of the most exciting recent discoveries in the interaction between operator algebras, geometry, topology, algebraic geometry and quantum groups in pure mathematics and algebraic and conformal field theory, string theory, statistical mechanics in theoretical physics. The primary objective of this Research Training Network is to ensure that there is a new generation of young researchers in Europe with sufficient breadth of knowledge and training required for this interdisciplinary research. This will be achieved through bringing them to the cutting edge of research across a broad front including the following Research Objectives: 1. Operator-algebras classification and structure 2. measure and isomorphism rigidity 3. free probability and random matrices 4. KK-theory and applications 5. cyclic theory and index theory 6. interplay between harmonic analysis and topology 7. quantum groups 8. applications to number theory 9. algebraic quantum field theory 10. fuzzy physics 11. strings and non-commutative geometry 12. quantum dynamics, quantum spin systems, quantum information The unifying mathematical concept behind the programme is the use of noncommutative operator algebras and noncommutative geometry to understand singular spaces or quantum spaces, replacing classical topological or measure spaces and the associated commutative algebras of continuous or measurable functions with noncommutative algebras of operators. Bringing together groups in Europe having a common goal in pursuing the deep connections between various branches of mathematics and physics we plan to address their conjectures and problems through a training network preparing young researchers equipped to work in operator algebras and noncommutative geometry.

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Coordinator

CARDIFF UNIVERSITY

Address

Newport Road 30-36
Cardiff

United Kingdom

Administrative Contact

David Emrys EVANS (Professor)

Participants (10)

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DUBLIN INSTITUTE FOR ADVANCED STUDIES

Ireland

KOBENHAVNS UNIVERSITET

Denmark

SYDDANSK UNIVERSITET.

Denmark

UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA

Italy

UNIVERSITETET I OSLO

Norway

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE (CNRS)

France

WESTFAELISCHE WILHELMS - UNIVERSITAET MUENSTER

Germany

KATHOLIEKE UNIVERSITEIT LEUVEN

Belgium

ERWIN SCHROEDINGER INSTITUT FUER MATHEMATISCHE PHYSIK - ESI

Austria

INSTITUTUL DE MATERMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Romania

Project information

Grant agreement ID: 31962

  • Start date

    1 June 2007

  • End date

    31 May 2011

Funded under:

FP6-MOBILITY

  • Overall budget:

    € 1 971 284

  • EU contribution

    € 2 803 297

Coordinated by:

CARDIFF UNIVERSITY

United Kingdom