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SUMMARY:Beyond the fundamental group - Philip Boalch (Paris)
DTSTART:20130212T160000Z
DTEND:20130212T170000Z
UID:TALK42292@talks.cam.ac.uk
CONTACT:Professor Maciej Dunajski
DESCRIPTION:Moduli spaces of representations of the fundamental group of a
  Riemann\nsurface have been studied from numerous points of view and appea
 r in\nmany parts of mathematics and theoretical physics. They form an\nint
 eresting class of symplectic manifolds\, they often have Kahler or\nhyperk
 ahler metrics (in which case they are diffeomorphic to spaces of\nHiggs bu
 ndles\, i.e. Hitchin integrable systems)\, and they admit\nnonlinear actio
 ns of braid groups and mapping class groups with\nfascinating dynamical pr
 operties. The aim of this talk is to describe\nsome aspects of this story 
 as well as its extension to the context of\nthe "wild fundamental group"\,
  which naturally appears when one\nconsiders {\\em meromorphic} connection
 s on Riemann surfaces. In\nparticular many new examples of complete hyperk
 ahler manifolds appear\nin this way\, some of which are familiar (without 
 the metrics) from\nclassical work on the Painleve equations.
LOCATION:DAMTP\, room MR11
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