Carlos Simpson

Title: Asymptotics of the Riemann-Hilbert correspondence and harmonic maps to buildings

Abstract:
We look at singularly perturbed systems of ODE's on a Riemann surface, with a given Higgs field as leading term.
The WKB asymptotics hold on a local scale. Using recent theory of Parreau and others, this leads to a
limiting harmonic map to an euclidean building. The differential of the harmonic map is given by the spectral curve
of the Higgs field. We then discuss our attempts to construct a universal such harmonic map with given spectral curve,
and the relation with Gaiotto-Moore-Neitzke spectral networks. This is joint work with Katzarkov, Noll and Pandit.