Sheared Pleated surfaces and Limiting Configurations for Hitchin’s equations
Abstract: A recent work by Mazzeo-Swoboda-Weiss-Witt describes a stratum of the frontier of the space of SL(2,C) surface group representations in terms of ‘limiting configurations’ which solve a degenerated version of Hitchin’s equations on a Riemann surface. We interpret these objects, originally defined gauge-theoretically, in terms of the hyperbolic geometric objects of shearings of pleated surfaces. The two perspectives are related via a third, the shapes of harmonic maps of surfaces. We aim to introduce the elements we need from each of the three areas. (Joint with Andreas Ott, Jan Swoboda, and Richard Wentworth.)