Abstract

This talk will give an introduction to multisymplectic geometry and homotopy moment maps. I will start from the basics, defining notions like n-plectic manifolds, Hamiltonian vector fields, and Hamiltonian (n-1)-forms. Then, before defining the Lie n-algebra of observables corresponding to an n-plectic manifold (definition due to C. Rogers), I will give a brief introduction to $L_{infty}$-algebras. Finally, I will introduce two notions of moment maps, the first one due to M. Callies, Y. Fregier, C. L. Rogers, and M. Zambon, and the second one due to J. Herman. If time permits, we will also compare the two notions (this last part would be based on joint work with L. Ryvkin).