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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

Attard Jérémy PhD candidate
Email
Bizi Nadir PhD candidate
Email
BULGAKOVA Daria PhD candidate
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 Email
Duval Christian Emeritus
+33.4.91.26.97.97 Email
Giovannetti Gabriel ATER
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
+33.4.91.26.97.94 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

94 results
Preprint, Working paper
T. Masson
La physique du XIXe siècle face au concept de paradigme
2017
Journal article
S. Khoroshkin, O. Ogievetsky
Diagonal reduction algebra and the reflection equation
Israël Journal of Mathematics, The Hebrew University Magnes Press, 2017, 221 (1), pp.705-729. 〈10.1007/s11856-017-1571-2〉
Journal article
C. Duval, T. Schücker
Gravitational birefringence of light in Robertson-Walker cosmologies
Physical Review D, American Physical Society, 2017, 96 (4), 〈10.1103/PhysRevD.96.043517〉
Preprint, Working paper
Bruno Iochum, Thierry Masson
Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori
2017
Preprint, Working paper
Robert Coquereaux
Theta functions for lattices of SU(3) hyper-roots
2017
Journal article
Christian Duval, G. W. Gibbons, P. A. Horvathy, P. -M. Zhang
Carroll symmetry of plane gravitational waves
Classical and Quantum Gravity, IOP Publishing, 2017, 34 (17), pp.175003. 〈http://stacks.iop.org/0264-9381/34/i=17/a=175003〉
Journal article
P.-M. Zhang, C. Duval, G.W. Gibbons, P.A. Horvathy
The memory effect for plane gravitational waves
Modern Physics Letters B, World Scientific Publishing, 2017, 772, pp.743 - 746. 〈https://www.journals.elsevier.com/physics-letters-b〉. 〈10.1016/j.physletb.2017.07.050〉
Master thesis
Varvara Petrova
Shuffle analogues for complex reflection groups G(m, 1, n)
Mathematical Physics [math-ph]. 2017
Preprint, Working paper
R. Coquereaux, Jean-Bernard Zuber
From orbital measures to Littlewood-Richardson coefficients and hive polytopes
2017
Journal article
Bruno Iochum, Thierry Masson
Heat trace for Laplace type operators with non-scalar symbols
Journal of Geometry and Physics, Elsevier, 2017, 116, pp.90-118. 〈10.1016/j.geomphys.2017.01.014〉
94 results

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