# Dr. Sebastian Heller (Universität Hamburg): "Higher solutions of Hitchin’s self-duality equations"

Jan 18, 2018 from 04:15 PM to 05:45 PM

LMS 4 - Raum 526 - Übungsraum

Abstract:

Solutions of Hitchin’s self-duality equations correspond to special real sections of the Deligne-Hitchin moduli space – twistor lines. A question posed by Simpson in 1995 asks whether all real solutions give rise to global solutions of the self-duality equations. An affirmative answer would allow for a complex analytic procedure to obtain solutions of the self-duality equations. The purpose of my talk is to explain the construction of counter examples given by certain (branched) Willmore surfaces in 3-space (with monodromy) via the generalized Whitham flow. Though these higher solutions do not give rise to global solutions of the self-duality equations on the whole Riemann surface M, they are solutions on an open dense subset of it. This suggest a deeper connection between Willmore surfaces, i.e., rank 4 harmonic maps theory, with the rank 2 self- duality theory. The talk is based on joint work with L. Heller.

Einladender: H. Weiß