Project with Eva Miranda and Philippe Monnier
We have invented a “hammer” called “abstract Nash-Moser normal form theorem” and now are looking for “nails” :-)
We used our hammer for the problem of rigidity of Hamiltonian actions on Poisson manifolds (see paper in Advances Math 2012). We don’t know yet to what problems (beyond Poisson stuff) can this theorem/method be applied
Apparently Michael Bailey (student of Gualtieri & Karshon in Toronto) could use our abstract theorem for the study of generalized complex structures in his thesis: www.math.toronto.edu/bailey/thesis.pdf
What about singular (or regular, for that matter) foliations, special metrics, embedding problems, pre-symplectic, Dirac structures, special solutions of dynamical systems, etc . ?