10 janvier : Mario Garcia-Fernandez (EPFL, Lausanne)
Titre : " Balanced metrics on twisted Higgs bundles "
A twisted Higgs bundle on a Kähler manifold X is a pair (E,\phi)
consisting of a holomorphic vector bundle E and a holomorphic bundle
morphism \phi: E \otimes M \to E for some vector bundle M. When M = TX and
\phi \wedge \phi = 0, such objects were considered by Hitchin when X is a
curve, and also by Simpson for higher dimensional base. There is a
Hitchin-Kobayashi correspondence which states that (E,\phi) is polystable
if and only if E admits a hermitian metric solving the Hitchin equations.
The Hitchin-Kobayashi correspondence is a powerful tool to decide whether
there exists a solution of the Hitchin equations, but it provides little
information as to the actual solution. Inspired by ideas of Luo and
Donaldson, in this lecture we discuss a quantization of this problem that
is expressed in terms of finite dimensional data and "balanced metrics"
that give approximate solutions to the Hitchin equations. This is joint
work with Julius Ross.