Valerio Melani: Poisson structures in derived algebraic geometry

Abstract:

Classically, a Poisson structure on a smooth manifold is a Poisson

bracket on the algebra of global functions, that is to say a Lie bracket

which is compatible with the product of functions. From a more

geometrical point of view, a Poisson structure is a bivector field

satisfying some properties. In this lecture we will explain how to

translate these two equivalent definitions in the world of derived

algebraic geometry, which studies spaces built up gluing simplicial

algebras.