(Ir)regular singularities and Quantum Field Theory

Events

| seminar

TQFT approach to meromorphic connections - Fission via irregular singularities

Speaker

Philip Boalch (Université Paris-Sud)

Abstract

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.

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