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SUMMARY:Algebraic Isomonodromic Deformations and the Mapping Class Group
DTSTART;VALUE=DATE-TIME:20200106T153000Z
DTEND;VALUE=DATE-TIME:20200106T164500Z
DTSTAMP;VALUE=DATE-TIME:20200224T081414Z
UID:indico-event-5460@indico.math.cnrs.fr
DESCRIPTION:The mapping class group acts on the set of representations mod
ulo conjugation of the fundamental group of n-punctured genus g-curves. Fo
r representations with values in SL(2\,C)\, finite orbits of this action h
ave been classified in the literature under various additional constraints
. We complete this classification by the remaining case of reducible repre
sentations for g>0. This study is motivated by the following result: up to
some minor technical conditions\, representations modulo conjugation with
values in GL(r\,C) that have finite orbit under the action of the mapping
class group are precisely those that appear as the monodromy of a logarit
hmic connection on the curve\, with poles at the punctures\, that admits a
n algebraic universal isomonodromic deformation. Both results concern a jo
int work with G. Cousin.\n\nhttps://indico.math.cnrs.fr/event/5460/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/5460/
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