Seminarium KMMF "Teoria Dwoistości"

There are several contexts in physics and differential geometry where a grading appears (the spin of particles, intensive/extensive variables, the exterior product of differential forms, etc.). It is thus natural to seek coordinates which are simultaneously homogeneous (i.e. respecting the grading) and adapted to the geometric structure under consideration. In the first part of my talk, I shall present a Frobenius theorem for involutive homogeneous distributions. In the second part, I shall present Darboux theorems for homogeneous presymplectic and Pfaffian forms. This is a work in progress with Prof. J. Grabowski.