Orateur(s) | Ian GROJNOWSKI - Université de Cambridge - I.M.J.,
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Titre | The Hodge theorem on infinite dimensional manifolds, and Ramanujan sums. |
Date | 12/05/2005 |
Horaire | 10:30 à 11:30 |
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Diffusion | |
Résume | In 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''. |
Salle | 11 rue Pierre et Marie Curie - 75005 Paris |
Adresse | |