Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...

A deformation U , of a graded K-algebra A is said to be of PBW type if grU is A. It has been shown for Koszul and N -Koszul algebras that the deformation is PBW if and only if the relations of U satisfy a Jacobi type condition. In particular, for these algebras the determination of the PBW property is a finite and explicitly determined linear algebra problem. We extend these results to an arbit...

Let α be a quadratic Poisson bivector on a vector space V . Then one can also consider α as a quadratic Poisson bivector on the vector space V ∗[1]. Fixed a universal deformation quantization (prediction of some complex weights to all Kontsevich graphs [K97]), we have deformation quantization of the both algebras S(V ∗) and Λ(V ). These are graded quadratic algebras, and therefore Koszul algebr...