Real projective structures on Riemann surfaces and hyper-Kähler metrics

Abstract

The non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, this enables one to relate geometric structures on surfaces with algebraic geometry, and on the other hand, one obtains interesting hyper-Kähler metrics on the solution spaces. In my talk, I will explain how to construct new hyper-Kähler metrics from certain singular solutions to Hitchin's self-duality equations. The main ingredients are graftings of projective structures, twistor spaces, and Deligne's notion of λ-connections.

Speaker

Research Interest

☑Harmonic maps, minimal and CMC surfaces

☑Geometric and analytic aspects of moduli spaces

☑Higgs bundles and Hitchin systems

☑Integrable systems

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