Séminaires : Groupes, Représentations et Géométrie

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We'll recall some basics about Slodowy slices, generalized slices in the affine Grassmannian, and quantizations thereof called W-algebras and Yangians, respectively, as well as their analogues for affine Lie algebras which are naturally described using the theory of vertex algebras. Then I'll explain a construction of vertex algebras associated to divisors in toric Calabi-Yau threefolds, which include affine W-algebras in type A for arbitrary nilpotents, and explain a partially conjectural dictionary between the geometry of the threefolds and the representation theory of these algebras.