Ruling out non-collapsed singularities in Riemannian 4-manifolds via the symplectic geometry of their twistor spaces

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• Fine, J (Universit Libre de Bruxelles)
• Thursday 23 July 2015, 14:00-15:00
• Seminar Room 2, Newton Institute Gatehouse.

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Metric and Analytic Aspects of Moduli Spaces

The twistor space of a Riemannian 4-manifold carries a natural closed 2-form. Asking that it be symplectic gives an interesting curvature inequality (which includes, for example, anti-self-dual Einstein metrics of non-zero scalar curvature). I will explain how the theory of J-holomorphic curves in the twistor space can be used to rule out certain types of degeneration in families of manifolds satisfying the curvature inequality. In particular, this shows that anti-self-dual Einstein metrics of negative scalar curvature cannot develop non-collapsed singularities. If there is time, I will end with speculation about other Riemannian uses for these symplectic structures and various conjectures concerning them.

This talk is part of the Isaac Newton Institute Seminar Series series.

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