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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
Other publication
Jean-Pierre Luminet
The Warped Science of Interstellar
The science fiction film, Interstellar, tells the story of a team of astronauts searching a dista.. 2015, pp.International Review of Science, vol.1(2)
Journal article
Christian Duval, P. A. Horvathy
Chiral fermions as classical massless spinning particles
Physical Review D, American Physical Society, 2015, 91 (4), pp.045013. 〈10.1103/PhysRevD.91.045013〉
Journal article
Razvan Gurau, Thomas Krajewski
Analyticity results for the cumulants in a random matrix model
Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, European Mathematical Society, 2015, 2 (2), pp.169-228. 〈10.4171/AIHPD/17〉
Journal article
Jean-Pierre Luminet
Cosmic Topology
Scholarpedia, San Diego, CA : Scholarpedia.org, 2015, 10 (8), pp.31544. 〈10.4249/scholarpedia.31544〉
Thesis
Jordan Francois
Réduction des symétries de jauge: une nouvelle approche géométrique
Mathematical Physics [math-ph]. Aix-Marseille Université, 2014. English
Conference paper
Jean-Pierre Luminet
Lemaitre's Big Bang
Frontiers of Fundamental Physics (FFP14), Jul 2014, Marseille, France. pp.214, PoS FFP14
Conference paper
Thomas Schucker
The Hubble diagram in a Bianchi I univers
2014 Maui conference on Subfactor Theory in Mathematics and Physics, dedicated to Vaughan Jones' 60th birthday, Jul 2014, Maui, Hawaii, United States. 2016
Journal article
Robert Coquereaux
Quantum McKay correspondence and global dimensions for fusion and module-categories associated with Lie groups
Journal of Algebra, Elsevier, 2014, 398, pp.Pages 258-283. 〈10.1016/j.jalgebra.2013.09.030〉
Book Section
François Jordan, Lazzarini Serge, Masson Thierry
Gauge field theories: various mathematical approaches
Eckstein, Michal; Heller, Michael; Szybka, Sebastian J. Mathematical Structures of the Universe, Copernicus Center Press, 2014, 978-83-7886-107-2
Journal article
Michal Eckstein, Bruno Iochum, Andrzej Sitarz
Heat trace and spectral action on the standard Podles sphere
Communications in Mathematical Physics, Springer Verlag, 2014, 332 (2), pp.627-668
109 results

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