Janina Bernardy (MPI Bonn)
According to Cariñena, Crampin, and Ibort multisymplectic structures are “the field theoretical analogues of the symplectic structures used in geometrical mechanics”. Multisymplectic geometry can therefore be used to study classical field theories from a geometric point of view but it also took on a mathematical life on its own being a generalization of symplectic geometry. Recent developments in the field of multisymplectic geometry like the definition of the $L_\infty$-algebra of Hamiltonian forms introduced by Rogers in 2012 and the introduction of homotopy momentum maps by Callies, Frégier, Rogers, and Zambon in 2016 provide a new starting point to reconsider long-standing conceptual problems in the understanding of symmetries of classical field theories.
In this talk I will provide a brief introduction to multisymplectic geometry as well as a crash course on Lagrangian field theory in the variational bicomplex on the infinite jet bundle. We will use this set-up to investigate homotopy momentum maps in Lagrangian field theory and the problem of reduction of multisymplectic structures with Hamiltonian symmetries.
This is joint work with Christian Blohmann and part of the talk is based on arXiv:2505.09492.
For more information and log in details please contact Christian Molle.
