Cohomology of hyperkähler moduli spaces via arithmetic
harmonic analysis -- Tamás Hausel

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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. 
In turn this will give a wealth of information on Betti numbers of
those hyperk&#228;hler moduli spaces, which
arise by a finite holomorphic symplectic quotient construction. These
include: toric hyperk&#228;hler varieties,
Nakajima's quiver varieties, Hilbert schemes of n points and moduli
spaces of instantons on C^2; 
GL(n,C) representation varieties of Riemann surfaces, and moduli
spaces of flat GL(n,C) connections on algebraic curves.