Topology Seminar: Noah Kieserman (Bowdoin)

Multiplicative differential forms are relevant whenever considering an object with a smooth groupoid of symmetries. One can ask what is the corresponding infinitesimal object, and in fact some of the most important examples arise from this direction. The geometric structures of Hamiltonian mechanics - Poisson manifolds, Dirac structures, etc. - can be viewed as infinitesimal data which, when integrated, yield multiplicative 2-forms on Lie groupoids.

I will explore the relationship between multiplicative structures on Lie groupoids and their infinitesimal counterparts on Lie algebroids.