School of Mathematics Colloquium
Kahler-Einstein metrics on Fano manifolds
by Prof. Ved Datar (University of California, Berkeley)
Thursday, January 11, 2018
from
to
(Asia/Kolkata)
at TIFR, MUMBAI ( AG-69 )
at TIFR, MUMBAI ( AG-69 )
Description |
Abstract - 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. |