Johannes Horn (Frankfurt): Spectral data for singular Hitchin fibers and asymptotic solutions to the Hitchin equation
Abstract: A recent breakthrough in the theory of Higgs bundle moduli spaces is the description of the asymptotics of the hyperkähler metric by Mazzeo-Swoboda-Weiss-Witt (MSWW) and Fredrickson (F). They show that (on the regular locus) its asymptotics are described by the semi-flat metric associated to the Hitchin system - a completely integrable system fibering a dense subset of the Higgs bundle moduli space by abelian torsors. In this talk, we will explain how one can describe degenerate Hitchin fibers by abelianisation on the normalized spectral curve and Hecke modifications at the singularities of the spectral curve. This naturally leads a construction of solutions to the decoupled Hitchin equation generalizing the limiting objects in the work of MSWW and F.