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Geometry, Physics, and Symmetries

Group “Fundamental Interactions”

Our activities are centered on the mathematical description of physical laws, in particular laws that govern fundamental interactions. The necessary tools are often of geometric, algebraic, combinatorial, analytic or functional nature. Some results or problems lead to the emergence of new mathematical structures needing a dedicated study. Others have direct physical applications.

Fundamental laws of nature, at the classical level, are naturally expressed in terms of geometry (for instance the notion of connection on a bundle appears in our understanding of both gravity and strong or electroweak interactions), and symmetries of the physical world are usually described, classically, by group theoretical constructions, in particular representation theory. Geometry finds its roots in the study of symmetries but one knows that mechanics itself uses geometry, in particular symplectic geometry, for its own formulation. A quantum description of physics requires not only the above tools but also appropriate generalizations of these notions. Approaches leading to theories of quantum gravity using non-commutative geometry, for instance, need mathematical descriptions where space-time (actually its algebra of functions) is replaced by a non-commutative algebra; moreover many developments of quantum field theory use generalizations of the notion of group, for instance supersymmetric theories use Lie super-algebras, and conformal field theory or string theory, as well as the theory of integrable systems, use concepts coming from affine Lie algebras and quantum groups.
Our activities focus around the above themes.

Directory of Members

BULGAKOVA Daria PhD candidate
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 Email
Iochum Bruno Emeritus
+33.4.91.26.97.96 Email
Krajewski Thomas University faculty
+33.4.91.26.95.61 Email
Lazzarini Serge University faculty
Chef de l’équipe « Géométrie, Physique et Symétries »
Web editor
Correspondant FRUMAM
+33.4.91.26.97.94 Email
Luminet Jean-Pierre Guest
+33.4.91.26.95.19 Email
Marsot Loïc PhD candidate
Email
Masson Thierry Researcher
Communications manager
Correspondant valorisation
+33.4.91.26.97.96 Email
Ogievetsky Oleg University faculty
+33.4.91.26.95.33 Email
Schücker Thomas University faculty
Chef du Groupe « Interactions fondamentales »
+33.4.91.26.95.61 Email
Triay Roland University faculty
+33.4.91.26.95.19 Email

List of Publications

109 results
Preprint, Working paper
Robert Coquereaux, Jean-Bernard Zuber
The Horn Problem for Real Symmetric and Quaternionic Self-Dual Matrices
2018
Journal article
S. Khoroshkin, O. Ogievetsky
Contravariant form for reduction algebras
Journal of Geometry and Physics, Elsevier, 2018, 129, pp.99-116. 〈10.1016/j.geomphys.2018.03.001〉
Preprint, Working paper
Jérémy Attard, J. François, S. Lazzarini, T. Masson
The dressing field method of gauge symmetry reduction, a review with examples
2018
Preprint, Working paper
Christian Duval, Johanna Pasquet, Thomas Schucker, Andre Tilquin
Gravitational birefringence and an exotic formula for redshift
2018
Preprint, Working paper
Bruno Iochum, Thierry Masson
Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori
2018
Conference paper
Christian Duval, Thomas Schucker
Gravitational birefringence of light at cosmological scales
Moriond conference on cosmology, Mar 2018, La Thuile, Italy
Conference paper
Jean-Pierre Luminet
Gravitational Music
17th Conference on Applied Mathematics APLIMAT 2018, Feb 2018, Bratislava, Slovakia. Slovak University of Technology in Bratislava in publishing house SPEKTRUM STU 17th Conference on Applied Mathematics APLIMAT 2018, pp.679-685, 2018, 〈http://evlm.stuba.sk/APLIMAT2018/proceedings/〉
Book Section
Céline Desmoulins, Jérémy Attard
SYNTHÈSE : 2017 : TABLE RONDE 2 INTER+SECTION : PARADIGMES
L' épistémologique et interdisciplinarité , A paraître, 〈http://www.amu-intersections.fr〉
Journal article
R. Coquereaux, Jean-Bernard Zuber
From orbital measures to Littlewood-Richardson coefficients and hive polytopes
Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, European Mathematical Society, 2018, Combinatorics, Physics and their Interactions, 5 (3), pp.339-386. 〈10.4171/AIHPD/57〉
Journal article
Robert Coquereaux
Theta functions for lattices of SU(3) hyper-roots
Experimental Mathematics, Taylor & Francis, 2018, 〈10.1080/10586458.2018.1446062〉
109 results

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