Integration of coupling Dirac structures
The main concern will be to describe the presymplectic groupoid integrating a coupling Dirac structure, with a particular attention to the so-called Yang-Mills-Higgs settings. Dirac structures are half way between symplectic and Poisson structures since they can be thought of as a foliation by presymplectic leaves. I will recall these notions and introduce the coupling version of a Dirac structure; these are strongly related with symplectic and Poisson fibrations. A particularly interesting situation they apply to is in a geometric description of the neighborhood of a coadjoint orbit.
