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BEGIN:VEVENT
UID:2019082306420720190909T15000020190909T1550005d60337f2ba3b@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20190823T114744
DTSTART:20190909T150000
DTEND:20190909T155000
SUMMARY:Geometry, Topology and Dynamics Seminar: Weighted cscK metrics and weighted K-stability, by Abdellah Lahdili
DESCRIPTION:Abdellah Lahdili (Montreal): Weighted cscK metrics and weighted K-stability We will introduce a notion of a K\"ahler metric with constant weighted scalar curvature on a compact K\"ahler manifold $X$, depending on a fixed real torus $\T$ in the reduced group of automorphisms of $X$, and two smooth (weight) functions defined on the momentum image of $X$. We will also define a notion of weighted Mabuchi energy adapted to our setting, and of a weighted Futaki invariant of a $\T$-compatible smooth K\"ahler test configuration associated to $(X, \T)$. After that, using the geometric quantization scheme of Donaldson, we will show that if a projective manifold admits in the corresponding Hodge K\"ahler class a K\"ahler metric with constant weighted scalar curvature, then this metric minimizes the weighted Mabuchi energy, which implies a suitable notion of weighted K-semistability. As an application, we describe the K\"ahler classes on a geometrically ruled complex surface of genus greater than 2, which admits conformally K\"ahler Einstein-Maxwell metrics. Please click here to make changes to, or delete, this seminar announcement.
LOCATION:636 SEO Chicago IL
CLASS:PRIVATE
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