117 citations · 600 across the 27 of their papers we have counts for
8 papers · 1 filter
Symplectic Manifolds and Isomonodromic Deformations
Philip Boalch
We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matr…
Riemann-Hilbert for tame complex parahoric connections
Philip Boalch
A local Riemann-Hilbert correspondence for tame meromorphic connections on a curve compatible with a parahoric level structure will be established. Special cases include logarithmi…
Irregular connections and Kac-Moody root systems
Philip Boalch
Some moduli spaces of irregular connections on the trivial bundle over the Riemann sphere will be identified with Nakajima quiver varieties. In particular this enables us to associ…
Some explicit solutions to the Riemann-Hilbert problem
Philip Boalch
Explicit solutions to the Riemann-Hilbert problem will be found realising some irreducible non-rigid local systems. The relation to isomonodromy and the sixth Painleve equation wil…
Quasi-Hamiltonian Geometry of Meromorphic Connections
Philip Boalch
For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as modu…
Wild nonabelian Hodge theory on curves
Olivier Biquard, Philip Boalch
On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles…