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 |
The gauge theoretical underpinnings of general relativity
100 Years of Gauge Theory, Jul 2018, Bad Honnef, Germany. pp.289-300, (10.1007/978-3-030-51197-5_12)
Contravariant form for reduction algebras
Journal of Geometry and Physics, 2018, 129, pp.99-116. (10.1016/j.geomphys.2018.03.001)
Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori
Journal of Geometry and Physics, 2018, 129, pp.1-24. (10.1016/j.geomphys.2018.02.014)
Gravitational birefringence and an exotic formula for redshift
Physical Review D, 2018, 97 (12), pp.123508. (10.1103/PhysRevD.97.123508)
Velocity Memory Effect for Polarized Gravitational Waves
Journal of Cosmology and Astroparticle Physics, 2018, pp.030. (10.1088/1475-7516/2018/05/030)
Plane partitions and their pedestal polynomials
Matematicheskie Zametki / Mathematical Notes, 2018, 103 (5-6), pp.793-796. (10.1134/S0001434618050115)
Hopf algebras and Tutte polynomials
Advances in Applied Mathematics, 2018, 95, pp.271-330. (10.1016/j.aam.2017.12.001)
Gravitational birefringence of light at cosmological scales
Moriond conference on cosmology, Mar 2018, La Thuile, Italy
Bimodule structure of the mixed tensor product over $U q s {\ell} ( 2 | 1 )$ and quantum walled Brauer algebra
Nuclear Physics B, 2018, 928, pp.217-257. (10.1016/j.nuclphysb.2018.01.010)
Gravitational Music
17th Conference on Applied Mathematics APLIMAT 2018, Feb 2018, Bratislava, Slovakia. pp.679-685
