Journée des Méthodes Géométriques en Mathématique Physique#

Le 8 septembre 2026 à Metz

IECL-Metz – Salle de séminaire

Programme#

Mardi, le 8 septembre 2026

• 10h30-12h00 Noriaki IKEDA (RIMS Kyoto et Ritsumeikan University) : Introduction to Courant sigma models
• 14h00-15h30 Simon-Raphaël FISCHER (Universität Göttingen) : Generalized Cartan geometry
• 15h30-16h00 Pause-café
• 16h00-17h30 Guillem CAZASSUS (IECL et Chinese University of Hong Kong) : Equivariant Floer homology

Organisation#

Véronique Chloup, Camille Laurent-Gengoux et Tilmann Wurzbacher

Soutien#

IECL, Projet Emergence/Exploratoire OAK de l’Université de Lorraine, Universität Göttingen.

Résumés#

• Introduction to Courant sigma models : A Courant algebroid is a 2-categorical generalization of Poisson and symplectic structures. We begin with the definition of a Courant algebroid and explain its construction in terms of a Q-manifold (a differential graded manifold), including the definition of a Q-manifold. Finally, we consider a physical theory based on a Courant algebroid, called the Courant sigma model, which is a generalization of Chern–Simons theory.
• Generalized Cartan geometry : It is well-known that a flat Cartan connection on a compact, connected and simply connected manifold M induces a Lie group structure on M. While one can locally find just any type of Lie group structure, a flat Cartan connection allows to glue the local pictures. On the other side, Cartan connections appear in recent works of singular foliations and (curved/generalised) Yang-Mills and Yang-Mills-Higgs theories; in those areas the Cartan connection appears without the flatness condition, but one still has a natural Lie algebra and group structure, so that we will discuss how to generalise known Cartan statements to a broader setting, pointing out compatibility structures to an underlying Lie algebra setting given by a deformed torsion. In other words, we will try to answer what structure is implied by a Cartan connection, even if it is not flat. This structure is known as twisted action algebroid, and this structure naturally sits in a generalised notion of Atiyah sequences: Sandglass sequences, whose splittings are Cartan connections (with certain curvature conditions). Not only that: If time permits, we will generalise Cartan connections to certain algebroid connections, and in that context a flat Cartan connection is then the obstruction for crossed modules of Lie groups, not just Lie group structures. In that way we will generalise Cartan geometry in such a way that its classical theorem also covers crossed modules.
• Equivariant Floer homology : I will present some constructions in Morse theory relevant to equivariant homology and involving A-infinity algebras (from arXiv:2404.17393 and arXiv:2505.01362). I will then discuss how to extend these constructions to various Floer theories, from a general prospective. If time permits, I will discuss a possible application to the Atiyah-Floer conjecture (work in progress with Conan Leung). [Je présenterai quelques constructions algébriques en théorie de Morse liées à l’homologie équivariante, impliquant des algèbres A-infinies (tirées de arXiv:2404.17393 et arXiv:2505.01362). Puis j’indiquerai de manière générale comment étendre ces constructions aux diverses théories de Floer. Si le temps le permet, je parlerai d’une application possible à la conjecture d’Atiyah-Floer (travail en cours avec Conan Leung).]