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Title:
TQFTs and Integrable systems: a geometric mystery
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Abstract:
The non-abelian Hodge correspondence provides a diffeomorphism between the moduli spaces of representations of the fundamental group of a Riemann surface and the moduli space of Higgs bundles. While the latter space is provided with a fibration that makes it an algebraically completely integrable system, which plays a key role in Mirror Symmetry, the algebro-topological properties of the former allow us to define new TQFTs. We will overview these ideas while giving a general introduction to the field. This talk is based in various work with I. Biswas, A. González-Prieto, V. Muñoz, P. Newstead and A. Peón-Nieto.
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