Schedule:

13:30 - 14:30. Daniele Valeri.

Title: Differential-difference equations and deformations of W-algebras.

Abstract: In this talk I will show that multiplicative lambda-brackets provide a convenient framework to study differential-difference equations. The main application is to the theory of q-deformations of W-algebras.

14:45 - 15:45. Anne Moreau.

Title: Singularities of nilpotent Slodowy slices and collapsing levels for W-algebras.

Abstract: When a simple affine W-algebra associated with a simple Lie algebra and a nilpotent element at level k is isomorphic to its affine vertex algebra, the level k is called collapsing. Collapsing levels have been intensively studied for the minimal nilpotent elements by Adamovic, Kac, Möseneder, Papi and Perse. However, only a little is known for other nilpotent elements. Using the singularities of nilpotent Slodowy slices and associated varieties of W-algebras, I will explain how to find new collapsing levels for non-minimal nilpotent elements. This is based on a joint work in progress with Tomoyuki Arakawa.

16:00 - 17:00. Alberto De Sole.

Title: Vertex algebra and Poisson vertex algebra cohomology.

Abstract: We present an operadic approach to vertex algebra cohomology. A general construction associates a cohomology complex to a linear operad. In the case of the chiral operads we get a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology.