We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an $L_{\infty}$-algebra, which is a cousin of the Koszul DGLA associated to a Poisson manifold. Its geometric understanding relies on ideas from Dirac geometry. Using this, we show that the infinitesimal deformations of pre-symplectic structures are obstructed.

In addition, we show that there is a strict morphism from this $L_{\infty}$-algebra to the one that controls the deformations of the underlying characteristic foliation, thereby linking the two deformation problems.

This talk is based on joint work with Florian Schätz.