# Centre de Physique Théorique

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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 Researcher +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 Luminet Jean-Pierre Guest +33.4.91.26.95.19 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

116 results
Preprint, Working paper
Oleg Ogievetsky, Senya Shlosman
Extremal Cylinder Configurations I: Configuration $C_{\mathfrak{m}}$
2019
Preprint, Working paper
Robert Coquereaux, Jean-Bernard Zuber
The Horn Problem for Real Symmetric and Quaternionic Self-Dual Matrices
2019
Preprint, Working paper
Oleg Ogievetsky, Senya Shlosman
The Six Cylinders Problem: $\mathbb{D}_{3}$-symmetry Approach
2019
Preprint, Working paper
Bruno Iochum, Thierry Masson
Heat coefficient $a_4$ for nonminimal Laplace type operators
2019
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〉
Preprint, Working paper
Nicolas Boulanger, Jordan Francois, Serge Lazzarini
A classification of global conformal invariants
2018
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
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〉
116 results

March 2019 :