Program

Opening

David Hernandez

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Timm Peerenboom

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Eric Opdam

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Xin Fang

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Alexandre Minets

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Pierre Baumann

Title: Some properties of the Mirković-Vilonen basis

Abstract: Let G be a complex connected reductive group. Under the Geometric Satake Equivalence, an irreducible representation V of G can be realized as the intersection homology of an affine Schubert variety. In this context, Mirković and Vilonen singled out algebraic cycles, whose classes form a basis of V. This basis shares many properties with the canonical basis of V, but the precise relationship between the two bases is not well understood.

Caroline Lassueur

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Balázs Szendroi

Title: Enumerative geometry of Quot schemes around the McKay correspondence and representation theory of affine algebras

Abstract: This talk will review some results computing generating series of Euler characteristics of certain singular Nakajima quiver varieties, spaces that can also be identified with Quot schemes of certain modules over cornered preprojective algebras. The proofs involve the study of collapsing fibres in the associated variation of GIT map, as well as (in type A) some combinatorics of coloured partitions, or (in arbitrary type) the study of quantum dimensions of standard modules over loop algebras following Nakajima. We will also point out some intricate representation theoretic questions that arise from the comparison of these two approaches. Based joint works with Lukas Bertsch, Alastair Craw, Søren Gammelgaard and Ádám Gyenge.