Noncommutative Poisson geometry and negative cyclic homology

par Alex Takeda (Institut des Hautes Etudes Scientifiques)

mardi 24 mai 2022, 14:00 → 15:00 Europe/Paris

IMT 1R2 207 (Salle Pellos)

Over the years there have been many different versions for the notion of a noncommutative Poisson structure. This talk will be about a structure proposed by Kontsevich and Vlassopoulos that generalizes all of these notions, called pre-Calabi-Yau structures, which can be defined for an A-infinity algebra. The spaces of such structures naturally have the structure of a simplicial set; in this talk I will explain how this structure is governed by negative cyclic homology in the case of a smooth algebra, by a correspondence which is a noncommutative version of the Legendre transform. Time allowing I will discuss some examples coming from topology and quivers.