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 |
Some Aspects Of Representation Theory Of Walled Brauer Algebras
Representation Theory [math.RT]. Aix Marseille Université, 2020. English. (NNT : )
SYNTHÈSE : 2017 : TABLE RONDE 2 INTER+SECTION : PARADIGMES
L' épistémologique et interdisciplinarité, , A paraître
Revisiting Horn's problem
Journal of Statistical Mechanics: Theory and Experiment, 2019, Special Issue in Memory of Vladimir Rittenberg, 2019 (9), pp.094018. (10.1088/1742-5468/ab3bc2)
Constructive Matrix Theory for Higher Order Interaction
Annales Henri Poincaré, 2019, 20 (12), pp.3997-4032. (10.1007/s00023-019-00845-9)
The SYK model and random tensors: Gaussian universality
19th Hellenic School and Workshops on Elementary Particle Physics and Gravity, Aug 2019, Corfu, Greece. pp.222, (10.22323/1.376.0222)
Multiplicities, pictographs, and volumes
13th International Workshop on Supersymmetries and Quantum Symmetries, Aug 2019, Yerevan, Armenia. pp.763-773, (10.1134/S1547477120050118)
Heat coefficient $a_4$ for non minimal Laplace type operators
Journal of Geometry and Physics, 2019, 141, pp.120-146. (10.1016/j.geomphys.2019.03.002)
Ulugh Beg, Prince of Stars
Science and Culture at the time of Amir Timur and Timurides, Apr 2019, Tashkent, Uzbekistan
An Illustrated History of Black Hole Imaging : Personal Recollections (1972-2002)
2019
The Dressing Field Method of Gauge Symmetry Reduction: Presentation and Examples
Geometric Methods in Physics XXXVI: Workshop and Summer School, Białowieża, Poland, 2017, pp.199-205, 2019, Trends in Mathematics, 9783030011567. (10.1007/978-3-030-01156-7_21)
