Deformations of pre-symplectic structures and generalized Koszul brackets

02.12.2016 15:15 - 17:00

Florian Schätz (Uni Luxemburg), Vortragsreihe: Simons Lecture Series on Mathematical Physics

 

Abstract: A pre-symplectic structure on a manifold is a closed two-form of constant rank. Pre-symplectic structures arise naturally in classical mechanics, for instance in the process of reduction. Moreover, they are closely related to coisotropic submanifolds and give rise to foliations. It is therefore an interesting problem to understand the space of all pre-symplectic structures of a given rank. I will describe a local parametrization of this space, as the set of Maurer-Cartan elements of an $L_{\infty}$-algebra. This parametrization is best understood in terms of Dirac geometry. The talk is based on joint work with Marco Zambon (KU Leuven).

 

 

Organiser:

N. Carqueville