AbstractIf C is a smooth projective complex curve, the nonabelian Hodge correspondence gives adiffeomorphism between the coarse moduli space of degree d rank r semistable Higgs bundles onC, and r-dimensional d-twisted representations of the fundamental group of the underlying Riemannsurface of C. lf r and d are not coprime, there are strictly semistables with nontrivial stabilizers, andit perha...
AbstractA classical theorem due to Birkhoff states that on a real or a complex symplectic manifold a function near its Morse critical point can be transformed by formal symplectomorphism into a power series in the pairwise sums of squares of the local coordinates, called its "Birkhoff normal form". A result of Sjöstrand says that, given certain conditions, one can compute the eigenvalues of the...
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