Seminarium KMMF "Teoria Dwoistości"

A multisymplectic manifold is a smooth manifold equipped with a closed and nondegenerate differential form of arbitrary degree. We begin with an exposition of the basic theory of multisymplectic manifolds, by analogy with the corresponding notions from symplectic geometry. We then review the Marsden-Weinstein symplectic reduction theorem and show how this result extends to the multisymplectic setting. For a special class of actions, we characterize the dependence of the reduced space on the reduction parameter, in a manner based on the symplectic Duistemaat-Heckman theorem. Finally, we present a multisymplectic extension of the Duistermaat-Heckman theorem. Finally, based on joint work with Antonio Miti and Leonid Ryvkin, we exhibit a reduction theorem for the L_\infty-algebra of observables associated to a premultisymplectic manifold. To take part in our seminar please use the following Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09