Colloquium Talk - Jakob Hultgren (UiO): Canonical Metrics in Complex Geometry
I will begin with a non-technical introduction to curvature of surfaces and then move on to the Uniformization Theorem which says that any Riemann surface can be deformed in a conformal way (i.e. preserving angles) into a Riemann surface of constant curvature. This theorem, which was proved in 1907, can be seen as the one-dimensional case of a problem in complex geometry going back to the 1930’s to determine which complex manifolds admits Kähler-Einstein metrics. Using the one-dimensional case as illustration, I will talk about an important milestone reached in 2013 when a conjecture (the Yau-Tian-Donaldson conjecture) relating existence of Kähler-Einstein metrics on projective manifolds to algebraic properties of the manifold was verified. I will end by talking about some more recent developments and some open problems in the field.
NB! Coffee/Tea/Biscuits from 14.00.