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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 Emeritus
+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
+33.4.91.26.97.94 Email
Marsot Loïc PhD candidate
Email
Masson Thierry Researcher
Communications manager
Correspondant valorisation
Correspondant LabEx Archimède
Correspondant FRUMAM
+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

122 results
Book
Bruno Iochum
Spectral Action in Noncommutative Geometry
Springer, 27, 2018, Springer Briefs in Mathematical Physics, 978-3-319-94787-7. ⟨10.1007/978-3-319-94788-4⟩
Journal article
Lluis Vena, Andrew Goodall, Thomas Krajewski, Guus Regts, LluÍs Vena
A Tutte Polynomial for Maps
Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2018, 27 (06), pp.913-945. ⟨10.1017/S0963548318000081⟩
Thesis
Jeremy Attard
Théories de jauge conformes, géométrie de Cartan et algébroïdes de Lie transitifs
Mathematical Physics [math-ph]. Aix Marseille Université, 2018. English
Journal article
Bruno Iochum, Thierry Masson
Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori
Journal of Geometry and Physics, Elsevier, 2018, 129, pp.1-24. ⟨10.1016/j.geomphys.2018.02.014⟩
Journal article
S. Khoroshkin, O. Ogievetsky
Contravariant form for reduction algebras
Journal of Geometry and Physics, Elsevier, 2018, 129, pp.99-116. ⟨10.1016/j.geomphys.2018.03.001⟩
Journal article
Christian Duval, Johanna Pasquet, Thomas Schucker, Andre Tilquin
Gravitational birefringence and an exotic formula for redshift
Physical Review D, American Physical Society, 2018, 97 (12), pp.123508. ⟨10.1103/PhysRevD.97.123508⟩
Journal article
Oleg Ogievetsky, Senya Shlosman
Plane partitions and their pedestal polynomials
Matematicheskie Zametki / Mathematical Notes, MAIK Nauka/Interperiodica, 2018, 103 (5-6), pp.793-796. ⟨10.1134/S0001434618050115⟩
Journal article
Thomas Krajewski, Iain Moffatt, Adrian Tanasa
Hopf algebras and Tutte polynomials
Advances in Applied Mathematics, Elsevier, 2018, 95, pp.271-330. ⟨10.1016/j.aam.2017.12.001⟩
Conference paper
Christian Duval, Thomas Schucker
Gravitational birefringence of light at cosmological scales
Moriond conference on cosmology, Mar 2018, La Thuile, Italy
Journal article
D.V. Bulgakova, A.M. Kiselev, I.Yu. Tipunin
Bimodule structure of the mixed tensor product over U q s ℓ ( 2 | 1 ) and quantum walled Brauer algebra
Nuclear Physics B, Elsevier, 2018, 928, pp.217-257. ⟨10.1016/j.nuclphysb.2018.01.010⟩
122 results

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