Abstract

The Deligne-Hitchin moduli space is the complex analytic reincarnation of the twistor space of thehyperkhler moduli space of solutions to the self-duality equations. Besides twistor lines, there arevarious other types of holomorphic sections satisfying a reality condition.These sections are usually related to solutions of certain integrable PDEs.Besides explaining these concepts and answering a question raised by Simpson, l will alsointroduce a natural energy functional on the space of sections and its relationship to thehyperholomorphic line bundle over the Deligne-Hitchin module space.

Speaker IntroPhD in 2008, Humboldt Universitt Berlin, Germany. Habilitation in 2014, Universitt Tbingen.Germany. Professor at Being Institute of Mathematical Sciences and Applications since 2022Research interests: minimal surfaces, harmonic maps, Riemann surfaces, Higgs bundles, modulispaces, visualisation and experimental mathematics.