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Arithmetic harmonic analysis, Macdonald polynomials and the topology of the Riemann-Hilbert monodromy map.

Lundi, 17 Octobre, 2005 - 12:30
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Résumé : 

We show that abelian and non-abelian Fourier transform over finite fields is the right tool to count solutions of holomorphic moment map equations over finite fields. Using the character theory of GL(n,F_q), due to Green and of gl(n,F_q) due to Letellier, this will give a wealth of information on Betti numbers of those hyperkähler moduli spaces, which arise by a finite holomorphic symplectic quotient construction.
These include: toric hyperkähler varieties, Nakajima's quiver varieties, Hilbert schemes of n points and moduli spaces of Yang-Mills instantons on C^2;
GL(n,C) representation varieties of Riemann surfaces, and moduli spaces of flat GL(n,C) connections on algebraic curves.
This is partly joint work with Emmanuel Letellier and Fernando

Thème de recherche : 
Algèbre et géométries
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