Group “Fundamental Interactions”
Our activities concern the mathematical description of physical laws, in particular those governing the fundamental interactions. The necessary tools are geometric, algebraic, combinatorial, or analytical in nature. Some problems lead to the emergence of new mathematical structures and require specific study. Others have immediate physical applications.
The laws of nature, at the classical level, are naturally expressed in geometric terms (the notion of a connection on a fiber bundle, for example, appears both in the formulation of the laws of gravitation and in those of the strong or electroweak interactions), and the symmetries of physics are described by constructions arising from group theory, in particular representation theory. Finally, it is well known that mechanics itself uses geometry—especially symplectic geometry—for its own formulation. At the quantum level, all these mathematical concepts must be generalized. Thus, approaches to quantum gravity using noncommutative geometry replace space-time (in fact the algebra of functions defined on it) with a noncommutative algebra, and many developments in quantum field theory use generalizations of the concept of a group: supersymmetric theories use Lie superalgebras, and conformal field theory, as well as string theory and integrable systems, relies on concepts from affine algebras and quantum groups. Our activities are focused on these themes.
| IOCHUM | Bruno | Research teacher emeritus | +33.4.91.26.97.95 | Contact |
| KRAJEWSKI | Thomas | Research teacher | +33.4.91.26.95.53 | Contact |
| LAZZARINI | Serge | Research teacher Team leader « Geometry, Physics, and Symmetries » | +33.4.91.26.97.94 | Contact |
| MASSON | Thierry | Researcher | +33.4.91.26.97.96 | Contact |
| OGIEVETSKY | Oleg | Research teacher emeritus | +33.4.91.26.95.33 | Contact |
| PORTELA | Leandre | Ph.D. | Contact | |
| TRIAY | Roland | Research teacher emeritus | +33.4.91.26.95.19 | Contact |
| USALA | Louis | Ph.D. | Contact |
Platonic Compounds of Cylinders
Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry, 103.2, pp.447, 2021, Proceedings of Symposia in Pure Mathematics, 978-1-4704-5592-7
Quantum Matrix Algebras of BMW type: Structure of the Characteristic Subalgebra
J.Geom.Phys., 2021, 162, pp.104086. (10.1016/j.geomphys.2020.104086)
On Schur problem and Kostka numbers
I. Krichever, S. Novikov, O. Ogievetsky and S. Shlosman. Integrability, Quantization, and Geometry : II. Quantum Theories and Algebraic Geometry. B.A. Dubrovin memorial volume., Volume 103.2, AMS, 2021, AMS Books series PSPUM/103.2, 978-1-4704-5592-7 978-1-4704-6435-6. (10.1090/pspum/103.2/01855)
Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection
Universe, 2021, 7 (1), pp.12. (10.3390/universe7010012)
Geometric studies of the interplay between spin and gravity
Mathematical Physics [math-ph]. Aix-Marseille Université, 2020. English. (NNT : )
On Horn's Problem and its Volume Function
Communications in Mathematical Physics, 2020, 376 (3), pp.2409-2439. (10.1007/s00220-019-03646-7)
Theta functions for lattices of SU(3) hyper-roots
Experimental Mathematics, 2020, 29 (2), pp.137-162. (10.1080/10586458.2018.1446062)
Fusion procedure for the walled Brauer algebra
Journal of Geometry and Physics, 2020, 149, pp.103580. (10.1016/j.geomphys.2019.103580)
On the Lévy-Leblond-Newton equation and its symmetries: a geometric view
Classical and Quantum Gravity, 2020, 37 (5), pp.055008. (10.1088/1361-6382/ab6998)
Cartan Connections and Atiyah Lie Algebroids
Journal of Geometry and Physics, 2020, 148, pp.103541. (10.1016/j.geomphys.2019.103541)
