Workshop on
Multisymplectic Structures
in Geometry and Physics

Lyon, France

A one-day forum on multisymplectic geometry and related topics.

date:  10 January, 2024
time:  10:00–17:00
institute:  Institut Camille Jordan, Université Claude-Bernard Lyon 1
room:  Fokko de Cloux, Bâtiment Braconnier

organizers:  Casey Blacker, Antonio Miti, Leonid Ryvkin

Francois Gieres  (Université Claude-Bernard Lyon 1)
Covariant phase space and multisymplectic geometry

We present the geometric formulation of explicitly time-dependent Hamiltonian systems in classical mechanics in order to motivate the consideration of multisymplectic geometry for obtaining a relativistically covariant canonical formulation of classical field theories. To conclude, the approach of (multi‑)symplectic geometry is briefly compared with the so-called covariant phase space approach.
Maxime Wagner  (Université de Lorraine)
The 6-sphere as a 2-plectic manifold

Firstly, we look at the 2-plectic form on the six-sphere which is strongly linked to the exceptional Lie group G_2 and show that there exists no Darboux theorem for this structure. In a second part, we will be interested in the dynamics associated with this structure.

Lunch break

Véronique Chloup and Phillippe Bonneau (Université de Lorraine)
An introduction to k-Poisson structures

Knowing what is Poisson geometry as a more general framework for symplectic geometry, what can be k-Poisson geometry as a more general framework for k‑plectic geometry? We'll describe quickly but completely the answer given by H. Bursztyn et al. to this question. We'll generalise the question to Dirac/k-Dirac (Dirac geometry being a larger generalisation of Poisson geometry) as an easy-to-reach and more complete point of view, that includes pre-k-plectic geometry. Seeing first a k-Poisson (resp. k-Dirac) manifold as the infinitesimal object associated to a k-plectic groupoid (resp. pre-k-plectic groupoid) we'll then give equivalent and more easy-to-use definitions as structures on the manifold itself, without any more reference to a groupoid. Finally, we'll present results about foliations of these structures and illustrate all this with examples.

Nothing in this talk will be original, all the material comes (mainly) from
- Bursztyn, Cabrera, Iglesias : "Multisymplectic geometry and Lie groupoids"
- Bursztyn, Martinez-Alba, Rubio : "On higher Dirac structures".
Casey Blacker (George Mason University)
Introduction to bundle gerbes

In this exposition, we approach bundle gerbes as smooth assignments of groupoids enriched in U(1)-torsors over a fixed manifold M. After first considering typical fibers, we present the general construction and proceed to define the Dixmier–Douady class, connective structures and surface holonomy.


Casey Blacker George Mason University
Antonio Miti Università Cattolica del Sacro Cuore
Leonid Ryvkin Université Lyon 1
Olga Kravchenko Université Lyon 1
Claude Roger Université Lyon 1
Francois Gieres Université Claude-Bernard Lyon 1
Sucheta Majumdar ENS de Lyon
Marco Valerio d'Agostino ENS de Lyon
Maxime Wagner Université de Lorraine
Véronique Chloup Université de Lorraine
Phillippe Bonneau Université de Lorraine