Orateur
Description
Via the Riemann-Hilbert correspondence, character varieties
can be seen as moduli spaces of monodromy data of meromorphic
connections with regular singularities on a Riemann surface. Varying the
curve with marked points, this leads to isomonodromic deformations and
to the well-known mapping class group actions on character varieties.
This story admits a far-reaching generalization if we do not restrict to
regular singularities: we now have to consider moduli spaces of
generalized monodromy data, giving rise to wild character varieties.
There are then new deformation parameters: the irregular types of the
connections at their singularities.
We will discuss some recent work, in collaboration with P. Boalch, G.
Rembado, and M. Tamiozzo, where we define and study the spaces of these
deformation parameters and their fundamental groups, yielding wild
mapping class groups. They act on the wild character varieties by
Poisson automorphisms, opening the door to many questions about these
wild dynamics.
