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

Presented by: 
J Fine Université Libre de Bruxelles
Date: 
Thursday 23rd July 2015 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
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.
Video for this talk will not be available due to technical errors. We pologise for the inconvenience
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons