Abstract We extend the Marsden–Weinstein–Meyer symplectic reduction theorem to the
setting of multisymplectic manifolds. In this context, we investigate the dependence of the …

A bstract We extend the notion of Lie bialgebroids for more general bracket structures used
in string and M theories. We formalize the notions of calculus and dual calculi on algebroids …

A bstract We construct a Poisson algebra of brane currents from a QP-manifold, and show
their Poisson brackets take a universal geometric form. This generalises a result of Alekseev …

Given a vector bundle A→ M we study the geometry of the graded manifolds T∗[k] A [1],
including their canonical symplectic structures, compatible Q-structures and Lagrangian Q …

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It has been a long standing question how to extend, in the finite-dimensional setting, the
canonical Poisson bracket formulation from classical mechanics to classical field theories, in …

We introduce a technique to realize brane wrapping and double dimensional reduction in
the context of Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) topological sigma …

We consider higher generalizations of both a (twisted) Poisson structure and the equivariant
condition of a momentum map on a symplectic manifold. On a Lie algebroid over a (pre-) …

In this thesis we use graded manifolds to study Poisson and related higher geometries
shedding light on many new aspects of their connection. The relation between graded …

We adapt the framework of geometric quantization to the polysymplectic setting. Considering
prequantization as the extension of symmetries from an underlying polysymplectic manifold …