Institut de Mathématiques de Luminy

Géométrie Non Commutative
et Physique Théorique
Séminaires communs GNC-CPT-LATP de la FRUMAM

Organisateurs : Michael Puschnigg, Thomas Krajewski et Andrei Teleman
Horaires : Le vendredi, à 14 h (en règle générale...) - Archives
Salle Séminaires : 3 ème étage, pièce 306 (en règle générale...)


vendredi 4 décembre
à 14h15
Sébastien Palcoux
(IML) :
Série discrète unitaire, caractères, fusion de Connes
et sous-facteurs pour l'algèbre Neveu-Schwarz

(présentation de son travail de thèse)

Résumé : On donne une preuve complète de la classification des représentations d'énergie positive unitaires de l'algèbre Neveu-Schwarz, de manière à obtenir directement les caractères de la série discrète. Ensuite, on explicite leurs règles de fusion de Connes, et on prouve que les sous-facteurs de Jones-Wassermann sont irréductibles d'indice fini; on donne les formules d'indice.

Lukasz Grabowski

vendredi 20 novembre
à 14h15
Lukasz Grabowski
(Goettingen) :
Recent progress on the Atiyah Conjecture

Abstract: In his paper from 1976, Michael Atiyah defined certain invariants of manifolds, so called L^2 Betti numbers. He also asked several questions about possible values of these numbers, which became to be collectively known as the Atiyah conjecture. It turned out that these questions are in fact questions about the group ring of the fundamental group of the manifold.In the talk I will first briefly discuss L^2 Betti numbers and their applications, and then describe the work (Grigorchuk-Zuk (2001), Dicks-Schick (2001)) which led to finding examples of (not finitely presented) groups which give rise to irrational L^2 Betti numbers (Austin (2009)).
In the next part I will describe the work in progress (Schick-Zuk, myself) which hopefully leads to finitely presented examples, and additionally gives information about what are the possible values of L^2-Betti numbers associated to finitely presented groups. Finally, I will talk about open questions concerning the L^2 Betti numbers.

vendredi 23 octobre
à 14h15
Michael Puschnigg
(IML, Marseille) :
Sous-algèbres isospectrales des C*-algèbres
de groupes hyperboliques

Abstract: Le point du départ du calcul des invariants homologiques d'une C*-algèbre est la construction d'une "bonne" petite sousalgèbre isospectrale.
On présentera une nouvelle construction des sousalgèbres isospectrales de la C*-algèbre réduite d'un groupe hyperbolique. On discutera des applications au calcul de la cohomologie cyclique de ces C*-algèbres et aux invariants L^2 délocalisés des variétés à courbure négative.

vendredi 25 septembre
à 14h15
Walther Paravicini
(Univ. Muenster) :
The Bost conjecture

Abstract: The Bost conjecture is the little sister of the renowned conjecture of Baum and Connes. Instead of computing the K-theory of the reduced C*- algebra of a group G, the Bost conjecture asserts an isomorphism of the K-theory of the L^1-algebra of G and the G-equivariant K-homology of underline{E}G. The conjecture has been proved by V. Lafforgue in many important cases.
We discuss what is known about permanence properties of the Bost conjecture, in particular we will consider the passage to subgroups and to direct limits. The main tool for the proof that the Bost conjecture passes to open subgroups uses constructions for groupoids which I am going to present in some detail.
If time permits, we will discuss how one could possibly generalise the Bost conjecture to allow for Banach algebra coefficients (so far, there is only an evident conjecture with C*-coefficients) which would be the first step for a proof of the passage of the Bost conjecture to direct products.

mercredi 10 juin
Roberto Trinchero
(Centro Atomico Bariloche, Argentine) :
Examples of non integer dimensional geometries

Abstract: Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative $C^{\star} $-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter dependent deformation of the canonical spectral triple over $S^{1}$. It's dimension spectrum includes real non-integer values. It has a non-trivial differential algebra and in contrast with the one dimensional case there are no junk forms for a non-vanishing deformation parameter. The distance on this space depends non-trivially on this parameter.

vendredi 27 mars
Johannes Huebschmann
(Lille 1) :
Espaces kählériens stratifiés, espaces hilbertiens costratifiés, et quantification kählérienne
en présence de singularités

mercredi 18 mars
Christoph Stephan
(Potsdam) :
Beyond the standard model:
a noncommutative approach

Abstract: Alain Connes' noncommutative geometry (NCG) allows to unify the classical Yang-Mills-Higgs theory and General relativity in a single geometrical framework.
This unification implies restrictions for the couplings of the Standard Model (SM) at a given cut-off energy which reduce the degrees of freedom compared to the classical SM.
I will give an introduction to the basic ideas of NCG and present models beyond the SM that are compatible with NCG and produce phenomenologically interesting extension of the SM. These extensions include the fermionic and the gauge sector as well as a recently discovered extension of the scalar sector.

jeudi 6 mars
Jean-Marie Lescure
(Clermont-Ferrand) :
Triplets spectraux pour les variétés à singularité conique


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