"Moment maps in diffeologies"
Abstract: I shall talk about a generalization of the "Moment Maps" to the category Diffeology. This construction applies to any smooth action of a diffeological group $G$ preserving a closed 2-form $omega$ defined on a diffeological space $X$. In particular, that reveals a legit universal moment map $mu_omega$, associated to the action of the whole group of automorphisms $Diff(X, omega)$. One of the originalities of the diffeological approach is that it avoids any reference to Lie algebra or any notion of vector fields but involves immediately the space of momenta of a diffeological group $G$,
that is, the space ${mathcal G}^*$ of left-invariant 1-forms on $G$. I will try to illustrate this construction with rigorous examples inspired by mathematical folklore.