TQFT approach to meromorphic connections---Fission via irregular singularities, Philip Boalch

Philip Boalch (Université Paris-Sud): "TQFT approach to meromorphic connections---Fission via irregular singularities"

I'll review the TQFT (quasi-Hamiltonian) approach to symplectic moduli spaces of irregular meromorphic connections on Riemann surfaces. Whilst the generic case was done in 2002 (arXiv:0203161), the general case was completed relatively recently in work with D. Yamakawa (arXiv:1512.08091). This generalises the approach to symplectic moduli spaces of flat connections of Alekseev-Malkin-Meinrenken, which corresponds to the tame (regular singular/Fuchsian) case. Their (quasi-classical) fusion operation is complemented by a new operation, fission, breaking the structure group. This involves a clean topological description of the Stokes phenomenon, generalising Stokes' original approach, as emphasised (and illustrated) in arXiv:1903.12612.