Séminaires : Séminaire Claude Chevalley

Equipe(s) :
Responsables :O. Brunat, M. Cabanes, et O. Dudas.
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Salle : 11 rue Pierre et Marie Curie - 75005 Paris
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Description

Orateur(s) Ian GROJNOWSKI - Université de Cambridge - I.M.J.,
Titre The Hodge theorem on infinite dimensional manifolds, and Ramanujan sums.
Date12/05/2005
Horaire10:30 à 11:30
Diffusion
RésumeIn this talk I'll begin by explaining that the Hodge theorem is false for even the simplest infinite dimensional manifolds (the affine flag varieties)--- there is a ``combinatorial obstruction'' to it holding. The correct statement implies new combinatorial identities generalising Ramanujan ${}_1\psi_1$ sums. These turn out to be equivalent to the Macdonald constant term conjectures (giving a new proof of a theorem of Cherednik). Then either I'll explain some more of the Hodge theoretic geometry of the affine flag variety, or some combinatorial shadows---the positivity of certain new symmetric functions. This is joint work with S. Fishel \& C. Teleman, its an introduction to ``math.AG/0411355''.
Salle11 rue Pierre et Marie Curie - 75005 Paris
Adresse
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