Beyond the fundamental group
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If you have a question about this talk, please contact Professor 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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