Quantisation of isomonodromy connections (Université Paris-Sud)

23.03.2018 14:00

Given a Riemann surface with marked points and some further decoration, one can construct a symplectic moduli space of meromorphic connections with prescribed polar divisor and normal forms at the poles. If the positions of the poles and the polar parts are varied, the monodromy data of the connections will, in general, vary as well: a deformation is isomonodromic when this does not happen, and such isomonodromic deformations are controlled by a system of nonlinear differential equations.

In this talk, we will consider a particular setup in genus zero, recall how to encode the isomonodromy connection in the flow of a time-dependent Hamiltonian system, and then deformation-quantise the system. The result is a new family of strongly flat connections generalising the Knizhnik-Zamolodchikov connection, as well as its derivation as a deformation quantisation of the Schlesinger system, i.e. the isomonodromy system for Fuchsian systems on the Riemann sphere.

This talk is based on the arXiv pre-print 1704.08616.

Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

entrée libre