# 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

 Coquereaux Robert Emeritus +33.4.91.26.95.18 Email Iochum Bruno Emeritus +33.4.91.26.97.95 Email Krajewski Thomas University faculty +33.4.91.26.95.53 Email Lazzarini Serge University faculty Chef de l’équipe « Géométrie, Physique et Symétries » Web editor +33.4.91.26.97.94 Email Marsot Loïc ATER Email Masson Thierry Researcher Communications manager Correspondant valorisation Correspondant LabEx Archimède Correspondant FRUMAM +33.4.91.26.97.96 Email NIEUVIARTS Gaston PhD candidate Email Ogievetsky Oleg University faculty +33.4.91.26.95.33 Email Schücker Thomas Emeritus +33.4.91.26.95.61 Email THIBAUT Jean PhD candidate +33.4.91.26.97.80 Email Triay Roland University faculty +33.4.91.26.95.19 Email

### List of Publications

132 results
Preprint, Working paper
Serge Lazzarini, Loïc Marsot
Conformal and projective tractors from 2-frame bundles by the dressing field method
2021
Preprint, Working paper
Thierry Masson, Gaston Nieuviarts
Derivation-based Noncommutative Field Theories on $AF$ algebras
2021
Thesis
Loïc Marsot
Études géométriques de l'interaction entre le spin et la gravité
Mathematical Physics [math-ph]. Aix-Marseille Université, 2020. English
Journal article
Oleg Ogievetsky, Senya Shlosman
Extremal Cylinder Configurations I: Configuration $C_{\mathfrak{m}}$
Discrete and Computational Geometry, Springer Verlag, In press, ⟨10.1007/s00454-020-00244-6⟩
Journal article
Robert Coquereaux
Theta functions for lattices of SU(3) hyper-roots
Experimental Mathematics, Taylor & Francis, 2020, 29 (2), pp.137-162. ⟨10.1080/10586458.2018.1446062⟩
Journal article
Robert Coquereaux, Colin Mcswiggen, Jean-Bernard Zuber
On Horn's Problem and its Volume Function
Communications in Mathematical Physics, Springer Verlag, 2020, 376 (3), pp.2409-2439. ⟨10.1007/s00220-019-03646-7#citeas⟩
Journal article
D.V. Bulgakova, Oleg Ogievetsky
Fusion procedure for the walled Brauer algebra
Journal of Geometry and Physics, Elsevier, 2020, 149, pp.103580. ⟨10.1016/j.geomphys.2019.103580⟩
Journal article
Serge Lazzarini, Loïc Marsot
On the Lévy-Leblond-Newton equation and its symmetries: a geometric view
Classical and Quantum Gravity, IOP Publishing, 2020, 37 (5), pp.055008. ⟨10.1088/1361-6382/ab6998⟩
Journal article
Jérémy Attard, Jordan François, Serge Lazzarini, Thierry Masson
Cartan Connections and Atiyah Lie Algebroids
Journal of Geometry and Physics, Elsevier, 2020, 148, pp.103541. ⟨10.1016/j.geomphys.2019.103541⟩
Thesis
Daria V. Bulgakova
Quelques aspects de la théorie des répresentations des algèbres de Brauer mure
Representation Theory [math.RT]. Aix Marseille Université, 2020. English
132 results

## Calendar

October 2021 :

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