Laboratoire de Physique
Theorique d'Orsay

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Bâtiment 210
Univ. Paris-Sud 11
91405 Orsay Cedex
France
T. 01 69 15 63 53
F. 01 69 15 82 87



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Agenda > Séminaires / Seminars > Mathématique Dernier ajout : jeudi 2 octobre 2014.

Séminaires Mathématique 2011-2012

Les séminaires se tiennent en salle 114 au 1er étage du bâtiment 210.

Seminars are held in room 114, 1st floor of Bdg 210.

Contact : Jean-Christophe Wallet.


-  Mercredi 4 Janvier, à 14h30, salle 114

Dimitri Gurevich (Laboratoire de Mathématiques et Applications, Université de Valenciennes) : From braided geometry to integrable systems

By Braided Geometry I mean a theory dealing with braidings (i.e. solutions of the Quantum Yang-Baxter Equation) playing the role of usual flips (or super-flips). The main object of Braided Geometry is the so-called Reflection Equation algebra associated to a given braiding. This algebra can be treated as an analog of the enveloping algebra U(gl(m|n)). Besides, for a matrix L coming in its defi-nition there is a version of the Cayley-Hamilton identity. This enables one to introduce "eigenvalues" of the matrix L. Also, a version of partial derivatives can be defi-ned on this algebra via a deep generalization of the Woronowicz’s differential calculus on a pseudogroup. By assuming the initial braiding to be a deformation of a super-flip, and passing to the limit q = 1 we get partial derivatives on the algebra U(gl(m|n)) (with a very surprising modi-cation of the Leibniz rule). This enables one to defi-ne analogs of the Laplacian operator and its higher counterparts on the algebra U(gl(m|n)). Such operators can be also de-fined on the braided deformation of this algebra (i.e. the corresponding Reflection Equation algebra). By restricting these operators to the center of the algebra in question and by expressing them via the aforementioned "eigenvalues" one can get a family of operators (hopefully, difference ones) in involution. They are two-parameter deformations of operators which are gauge equivalent to Calogero-Moser ones. I plan to exhibit the simplest example in details.

-  Mercredi 7 Décembre, à 14h30, salle 114

Jean Savinien (Laboratoire de Mathématiques et Applications, Université de Metz) : Triplets spectraux et ordre apériodique

Un sous-shift minimal et apériodique est un modèle symbolique (unidimensionnel) de solide apériodiquement ordonné. Une des plus fortes notions d’ordre apériodique correspond au cas des puissances bornées : quand le nombre de répétitions consécutives de chaque mot fini est uniformément borné. Nous construisons une famille de triplets spectraux (structures riemanniennes non commutatives) pour un sous-shift minimal et apériodique, et étudions la famille des métriques associées (distances de Connes). Nous montrons que le sous-shift est à puissances bornées si et seulement si les métriques inf et sup sont Lipschitz équivalentes. Travail en collaboration avec J. Kellendonk (Lyon 1) et D. Lenz (Jena, Allemagne).

-  Mercredi 16 Novembre, à 14h30, salle 114

Jesper Grimstrup (Niels Bohr Inst., Copenhagen Univ.) : Coupling matter to quantum gravity via noncommutative geometry

In my talk I will first observe that natural non-commutative structures reside within the setup of canonical quantum gravity. I will then present a specific noncommutative geometry based on this observation, namely a spectral triple over an algebra of holonomy loops. The spectral triple is essentially a reorganization of the basic elements of loop quantum gravity, and as such it encodes the kinematics of quantum gravity. Finally, I will show that this construction involves a natural class of semi-classical states which entail matter couplings in a semi-classical approximation.