Twistor spaces were originally devised as a way to use techniques of complex geometry to study 4-dimensional Riemannian manifolds. In this talk I will show that they also make it possible to apply techniques from symplectic geometry. In the first part of the talk I will explain that when the 4-manifold satisfies a certain curvature inequality, its twistor space carries a natural symplectic structure. In the second part of the talk I will discuss some results in Riemannian geometry which can be proved via the symplectic geometry of the twistor space. Finally, if there is time, I will end with some speculation
about potential future applications, involving Poincaré—Einstein 4-manifolds, minimal surfaces and distinguished closed curves in their conformal infinities
Seminar series
Date
Mon, 20 Feb 2017
Time
14:15 -
15:15
Location
L4
Speaker
Joel Fine
Organisation
Universite Libre de Bruxelles