# Séminaires : Séminaire Groupes, Représentations et Géométrie

 Equipe(s) : gr, Responsables : A. Brochier, O. Brunat, J.-Y. Charbonnel, O. Dudas, E. Letellier, D. Juteau, M. Varagnolo, E. Vasserot Email des responsables : Adrien Brochier , Olivier Brunat , Jean-Yves Charbonnel , Olivier Dudas , Emmanuel Letellier , Daniel Juteau , Michela Varagnolo , Eric Vasserot Salle : salle 2015, 2em étage, Adresse : Sophie Germain Description

 Orateur(s) Ivan CHEREDNIK - University of North Carolina-Chapel Hill, Titre Motivic and DAHA superpolynomials in any ranks for plane curve singularities Date 24/05/2019 Horaire 14:00 à 15:00 Résume There was not much progress with the extension of theory of (moduli spaces of) vector bundles from smooth to singular curves. Surprisingly, this can be managed in a rather elementary way for plane curve singularities. The corresponding moduli spaces will be described; they generalize compactified Jacobians (the case of rank one). This theory is closely related to nil-elliptic affine Springer fibers (in type A'') with non-reduced spectral curves, their germs to be exact. The corresponding motivic superpolynomials are expected to coincide with colored (by columns) DAHA superpolynomials, which is checked sufficiently well. The former can be defined for any curve singularities but the connection to the latter is so far only in the planar case. A possible implication is to Hall-Ringel convolution algebras for curve singularities. This can potentially provide a variant of elliptic Hall algebras by Burban-Schiffmann-Vasserot for any (arithmetic) genus upon the restriction to curve singularities. The talk will require almost no knowledge of rings and modules; the DAHA superpolynomials will be defined. Salle salle 2015, 2em étage, Adresse Sophie Germain