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Moduli spaces of representations
The moduli space of representations of the fundamental group of a compact surface in a Lie group has a tremendously reach geometry relating to symplectic geometry, hyperkaehler geometry, integrable systems, Teichmueller theory, etc. This space can be interpreted in purely differential-geometric terms as a moduli space of flat connections. Moreover, by choosing a complex structure on the surface, it can be identified with a moduli space of holomorphic objects known as Higgs bundles over the resulting Riemann surface. After explaining these correspondences, we will illustrate the power of the holomorphic point of view to study the topology of the moduli spaces.
Thursday, October 14, 2004, 245 Altgeld Hall, 4 p.m.
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