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Beyond the fundamental group

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If you have a question about this talk, please contact Dr Maciej Dunajski.

Moduli spaces of representations of the fundamental group of a Riemann surface have been studied from numerous points of view and appear in many parts of mathematics and theoretical physics. They form an interesting class of symplectic manifolds, they often have Kahler or hyperkahler metrics (in which case they are diffeomorphic to spaces of Higgs bundles, i.e. Hitchin integrable systems), and they admit nonlinear actions of braid groups and mapping class groups with fascinating dynamical properties. The aim of this talk is to describe some aspects of this story as well as its extension to the context of the “wild fundamental group”, which naturally appears when one considers {\em meromorphic} connections on Riemann surfaces. In particular many new examples of complete hyperkahler manifolds appear in this way, some of which are familiar (without the metrics) from classical work on the Painleve equations.

This talk is part of the Mathematical Physics Seminar series.

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