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Kahler-Einstein metrics on Fano manifolds

Dr. Ved Datar University of California, Berkeley
Dr. Ved Datar University of California, Berkeley
When Jan 02, 2018
from 04:00 PM to 05:00 PM
Where LH 006
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Abstract: A version of the uniformization theorem states that any compact Riemann surface admits a metric of constant curvature. A deep and important problem in complex geometry is to characterize Kahler manifolds admitting constant scalar curvature Kahler (cscK) metrics or extremal Kahler metrics. Even in the special case of Kahler-Einstein metrics, starting with the work of Yau and Aubin in the 1970's, a complete solution was obtained only very recently by Chen-Donaldson-Sun (and Tian). Their main results says that a Fano manifold admits a Kahler-Einstein metric if and only if it is K-stable. I will survey some of these recent developments, and then focus on a refinement obtained in collaboration with Gabor Szekelyhidi. This has led to the discovery of new Kahler-Einstein manifolds. If time permits, I will also talk about some open problems on constructing cscK and extremal metrics on blow-ups of extremal manifolds, and mention some recent progress.

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