operator algebras and noncommutative geometry

Topics : operator algebras and group representations; their connections with topology, geometry, probability theory, ergodic theory, number theory and theoretical physics.

NOTE: operator algebras = von Neumann algebras + K-theory + cyclic cohomology, the noncommutative versions of measure theory, topology and differential geometry.

Mode of operation : around two transverse seminars, GNCPT (Noncommutative Geometry and Theoretical Physics) and GVN (Gromov-von Neumann seminar on geometry and analysis) run jointly between the IML, the CPT and the LATP.

Researchers in operator algebras: Kasparov, Puschnigg, Wassermann, Zekri, graduate students : El Morsli, Fuchs, Palcoux.

Associated project : The GAP project (2003-2006), "Géométrie, Algèbres d'opérateurs, Physique", a special direct action of the CNRS, coordinated by Schücker (CPT), Short (LATP) and Wassermann (IML). In addition to monthly meetings, the project has the educational goal of assuring basic courses in geometry and physics at the master's level. It is probable that an extension of the project will be requested for 2007.

Associated seminars :

GNC/PT (noncommutative geometry, theoretical physics) organised by Schücker [Krajewski] (CPT), Teleman [Pittet] (LATP) and Wassermann [Puschnigg] (IML) is a weekly seminar that evolved in a natural way from a long-established seminar in operator algebras and group representations that has been running in Luminy for over 25 years. The theme of the seminar is noncommutative geometry, interpreted in the broadest possible sense. The seminar attracts between 15 and 35 participants, depending on the topic.

GVN (Gromov-von Neumann seminar on geometry and analysis) organised by Pittet, Short, Yeganefar (LATP) and Puschnigg, Wassermann (IML). This new weekly activity is devoted to the area of research between the geometry of groups and algebra operators. It began in January 2006 and attracts between 10 and 15 participants.

Doctoral course : Starting in February 2006 Wassermann has given a doctoral course on "Analysis of Operators" each Tuesday from 2.00-3.30 pm at the CMI. This course is about Toeplitz determinants and their connections with random matrices, the Ising model, multiplicative aspects of nonommutative geometry and boson-fermion duality in conformal field theory. This course will also be given in the Michaelmas term 2006 as a Part III course in the Cambridge Mathematical Tripos in connection with the half-year meeting on Noncommutative Geometry at the Newton Institure, organised by Connes and Majid.

Invitations : In addition to invitations to the two common seminars, for a number of years there have been longer term invitations to scientists of mutual interest to mathematicians and physicists. Voiculescu, Jones, and Shlyakhtenko received one-month university invitations; Recknagel and Cherednik received CNRS visiting positions through the FRUMAM between the IML and the CPT; and Popa, Schick and Varilly were invited in conjunctions with the GNC2004 event at CIRM. Currently all activities in operator algebras and noncommutative geometry in Marseille are administered directly through the 3 departments concerned (the IML, the CPT and the LATP).