Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Smooth and Pre-Calabi-Yau structures in string topology

I will present some recent joint work with Kontsevich and Vlassopoulos that deals with the relation between smooth Calabi-Yau structures and pre-Calabi-Yau structures. This relation can be thought of as a noncommutative version of the relation between symplectic structures and nondegenerate Poisson structures, is an analog of the Legendre transform, and is described in terms of a graphical calculus. One of the examples where this formalism can be applied is the topology of loop spaces; time allowing, I will discuss an extension of this formalism to algebraic string topology operations.