Robert Coquereaux   Web pages


Robert Coquereaux
Directeur de Recherche au CNRS

Physicien théoricien au  Centre de Physique Théorique  (CPT)
Case 907. Luminy.  13288. Marseille.
France.

Version francaise


Curriculum Vitae & Publication list



 

Some of my papers in html (hypertext), ps or pdf


Video : Espaces fibrés et interactions fondamentales (1h.) :
Lecture given at the M.S.H, Paris, 2005. Conference "Fibrés, fibrations et connexions" (coll. Les archives audiovisuelles de la recherche)


Livre HyperTexte -- HyperText Book:

ESPACES FIBRES ET CONNEXIONS
Un livre de géométrie différentielle en hypertexte
A book of differential geometry in hypertext (sorry, the english version is not available)
Ce livre est une introduction à la théorie des espaces fibrés. Il est destinés aux jeunes (et aux moins jeunes) voulant découvrir les structures mathématiques qui se situent à la base de notre compréhension des théories physiques contemporaines. Il s'adresse donc, a priori , à un public d'étudiants en physique théorique mais il peut également constituer une introduction aux idées en question pour les jeunes mathématiciens, et plus généralement pour les curieux possédant un bagage mathématique suffisant (niveau requis égal ou supérieur à celui qu'on acquiert , en France, dans les classes de Mathématiques Spéciales ou à l'issue du DEUG A). L'accent est essentiellement mis sur la théorie des espaces fibrés et celle des connexions, ainsi que sur la géométrie riemanienne, mais les deux premiers chapitres contiennent un résumé de notions générales concernant les variétés différentiables, les groupes et les algèbres de Lie. Le dernier chapitre est une introduction à la géométrie non commutative. Le style est volontairement informel. Si vous cherchez à lire un résumé hyper-dense, ceci n'est pas pour vous. Dans sa forme actuelle, l'ouvrage ne contient aucune description de la géométrie des varétés graduées (super-géométrie). Ce thème sera ultérieurement incorporé à l'ouvrage. La première version html a été mise sur l'internet en mai 1997.La version html actuellement disponible est la version 3.00 (mai 2002).La version ps actuellement disponible est la version 3.00 (mai 2002).
Mots clefs : variétés, groupes de Lie, algèbres de Lie, actions de groupes, espaces homogènes, espaces fibrés, connexions, dérivées covariantes, courbure, champs de jauge, Yang-Mills, Relativité Générale, interactions fondamentales, gravité, géométrie non commutative.
Keywords : manifolds, Lie groups, Lie algebras, group actions, homogeneous spaces, fiber bundles, connections, covariant derivatives, curvature, gauge fields, Yang-Mills, General Relativity, fundamental interactions, gravity, noncommutative geometry.


Organised conferences

Infinite Dimensional Geometry, Non Commutative Geometry, Operator Algebras and Fundamental Interactions
First Carribean Spring School of Mathematics and Theoretical Physics.
 Saint-François, Guadeloupe (31 mai - 13 juin 1993)

Quantum symmetries in theoretical physics and mathematics
Simetrías cuánticas en física teórica y en matemática
Symétries quantiques en physique théorique et en mathématiques

BARILOCHE 2000: A CIMPA-UNSA-UNESCO-ARGENTINA SCHOOL S.C. de Bariloche, Patagonia, Argentina (10 - 22 janvier 2000)
Available lectures ( download ) : N. Andruskiewitsch, M. Dubois-Violette, D. Evans, A. Ocneanu, O. Ogievetsky, J.B. Zuber.
Available poster: Classification of SL(2,C) and SL(3,C)  quantum subgroups by A. Ocneanu, poster presented at the Bariloche school (January 2000), in relation with the classification of  SU(3) lattice integrable models (P. Di Francesco - J.B. Zuber ).
Lecturers (photos) N. Andruskiewitsch, M. Dubois-Violette, D. Evans, A. Ocneanu, O. Ogievetsky, N. Reshetikhin, M. Rosso, A. Varchenko, S.L. Woronowicz, J.B. Zuber.

Geometry and Integrability in Mathematical Physics : GIMP'08
Marseille, 15-19 septembre 2008
Poster

Symplectic Geometry and Quantum Symmetries in Mathematical Physics
Hsinchu, NCTS, 21-25 fevrier 2011
NCTS-CPT Joint Workshop. National Center for Theoretical Sciences, Hsinchu, Taiwan.
Poster


Warning : The following bookmarks are often rather old...

Mathematics & Theoretical Physics : bookmarks
Quantum field theory
Elementary particles
Classical and quantum gravity
Cosmology
Differential and riemannian geometry
Lie groups, etc.
Quantum groups and quantum groupoids
Non Commutative Geometry
Comments on Physics, Mathematics, Life, the Universe and Everything

Computers
 
Lisp and Ivory machines (links)
The last link is a memo explaining how to send an X11 window from a (very old) Ivory Lisp Machine running Genera to a (not so new) Apple G5 running OSX

Photos

Travels
Diving (video Tuamotu)

Links
PageWebPons CPT CIRM CERN-TH
Marseille : hotels, restaurants, history, things to do (from Guide du Routard, access restricted to specific machines within the CPT...)

What about diving (zoom!) into a fractal tiling of order 7 ?  
If you want to know...

Fusion graphs

To every Dynkin diagram G and to every positive integer k (level), one associates a fusion category that can be described either in terms of integrable representations of affine Lie algebras, or in terms of a particular class of representations of quantum groups at roots of unity. Fusion by fundamental integrable representations can be described by graphs called (fundamental) "fusion graphs". These fusion categories somehow generalize, at the quantum level, the theory of representations of Lie groups and Lie algebras, and the process of "fusion" replaces the usual notion of tensor product of representations. The web pages that are given (here) show fusion graphs of type (G,k) and describe some of their properties, for all types of Dynkin diagrams (of small rank), and for various values of the level.
Fusion graphs associated with the other irreducible integrable representations (not necessarily fundamental) can also be drawn, see the example below.

Fusion graphs for quantum modules and quantum subgroups

Classically, every finite subgroup of a Lie group possesses its own theory of representations, and the space obtained by considering sum of irreducible representations is a module over the representation ring associated with the chosen Lie group. Something similar exists in the quantum framework: for every fusion category of type (G,k) one can consider "module-categories" (not to be confused with modular categories) on which the previous one, which is monoidal, acts. Action of (G,k) on a chosen module can itself be described by a graph. See (here) the lectures given at the school of Bariloche 2000, and in particular the contribution of A. Ocneanu describing the classification of quantum modules and quantum subgroups of G=SU(2), SU(3), and SU(4). Our web pages (there) summarize these classifications and give other examples for other choices of G.

In physics, one knows how to associate particular quantum field theories (conformal field theories of type WZW) to fusion categories defined by the couple (G,k) where G is a Dynkin diagram (describing a Lie group) and k is a non negative integer called the level. Another possibility is to associate a theory to the fusion category defined by the quantum double of a finite group, or more generally to a pair (H,w ) where w is a U1 valued 3-cocycle on H. Even more generally one can consider orbifolds models defined by a Lie group, some level, and a finite subgroup.
Associated module-categories may be called "quantum subgroups" or "quantum modules". They can be described by fusion graphs. They possess their own interpretation in the framework of boundary conformal field theories. In particular, one knows, for every one of them, how to define and calculate a modular invariant quantity that is interpreted as a partition function.

Character tables (modular data) for quantum doubles of finite groups

This file contains modular data for Drinfeld doubles of finite groups, also called (untwisted) quantum doubles of finite groups.
In particular it contains modular data for all exceptional finite subgroups of SU2, SU3, and for a few members belonging to their infinite series of sugbroups.


Centre de Physique Théorique Centre International de Rencontres Mathématiques

Clef de l'univers accrochée à la lune

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