You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar
Speaker: Craig van Coevering (Boğaziçi)
“Extremal Kähler metrics and the moment map”
Abstract: An extremal Kähler metric is a canonical Kähler metric, introduced by E. Calabi, which is somewhat more general than a constant scalar curvature Kähler metric. The existence of such a metric is an ongoing research subject and expected to be equivalent to some form of geometric stability of the underlying polarized complex manifold (M,J,[ω]) –the Yau-Tian-Donaldson conjecture. Thus it is no surprise that there is a moment map, the scalar curvature (A. Fujiki, S. Donaldson), and the problem can be described as an infinite dimensional version of the familiar finite dimensional G.I.T.
I will describe how the moment map can be used to describe the local space of extremal metrics on a symplectic manifold. Essentially, the local picture can be reduced to finite dimensional G.I.T. In particular, we can construct a course moduli space of extremal Kähler metrics with a fixed polarization [ω]∈H2(M,R), which is an Hausdorff complex analytic space
Date: Friday, 14 April 2023
Time: 15:40 (GMT+3)
Place: Zoom
This is an online seminar. To request the event link, please send a message to sertoz@bilkent.edu.tr