26 citations · 41 across the 3 of their papers we have counts for
4 papers
Six results on Painleve VI
Philip Boalch
After recalling some of the geometry of the sixth Painleve equation, we will describe how the Okamoto symmetries arise naturally from symmetries of Schlesinger's equations and summ…
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…
From Klein to Painleve via Fourier, Laplace and Jimbo
Philip Boalch
We will describe a method for constructing explicit algebraic solutions to the sixth Painleve equation, generalising that of Dubrovin-Mazzocco. There are basically two steps: First…
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…