Olivier Brahic, Instituto Superior Técnico
On higher analogues of symplectic fibrations

One can obtain simple models for abstract field theories by looking at closed forms defined on the total space of a fibration. For instance, in the case of hamiltonian fibrations, this is how Weinstein recovered Sternberg's minimal coupling, yielding a geometrical context for classical Yang-Mills theories. More generally, one can introduce 2-plectic fibrations and interpret the equations for coupling in terms of higher analogues of connections.
Support: FCT, CAMGSD, New Geometry and Topology.