Speaker
Description
Let $G$ be a complex reductive Lie/algebraic group. Certain (de Rham) moduli spaces of regular singular meromorphic connections, defined on principal G-bundles over the Riemann sphere, have natural (complex) Poisson/symplectic structures. These can be deformation-quantised, and generically lead to spaces of (co)invariants for tensor products of Verma modules for $\mathfrak{g} = Lie(G)$: in turn, they are related to spaces of (co)vacua for the affine version of g, towards the usual conformal blocks of the Wess--Zumino--Novikov--Witten (WZNW) model in 2d conformal field theory.
Moreover, upon deforming the position of the simple poles of the meromorphic connections in admissible fashion, a Poisson/symplectic braid-group action arises on the (Betti) moduli spaces of monodromy data, viz. the $G$-character varieties of punctured spheres; and this action was later interpreted as the semiclassical limit of the Drinfel'd--Kohno braiding, i.e. precisely the monodromy of the flat vector bundle of WZNW conformal blocks.
In this talk we will aim at a review of part of this story, and then present extensions about irregular singular meromorphic connections.
In alphabetical order, this is past/present work with P. Boalch, D. Calaque, J. Douçot, G. Felder, M. Tamiozzo, and R. Wentworth.
