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UID:7566@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170425T140000
DTEND;TZID=Europe/Paris:20170425T150000
DTSTAMP:20241120T204411Z
URL:https://www.i2m.univ-amu.fr/evenements/extremal-kahler-metrics-and-don
 aldsons-quantisation/
SUMMARY:Yoshinori Hashimoto (I2M\, Aix-Marseille Université): Extremal Kä
 hler metrics and Donaldson’s quantisation
DESCRIPTION:Yoshinori Hashimoto: Kähler metrics with “optimal” curvatu
 re properties have been studied intensively since the proposal of E. Calab
 i\, who suggested that we look for Kähler metrics whose L^2-norm of the s
 calar curvature is minimal. These metrics are called extremal\, and includ
 e as subclasses the constant scalar curvature Kähler (cscK) metrics and K
 ähler-Einstein metrics. Extremal Kähler metrics are actively studied\, p
 articularly in connection to the algebro-geometric stability of the underl
 ying Kähler manifold\, following the proposal of S.-T. Yau\, G. Tian\, S.
  Donaldson\, and G. Székelyhidi.\nA foundational result in this area is D
 onaldson’s quantisation\, which provides a “finite dimensional” appr
 oximation of cscK metrics when the automorphism group is discrete. Several
  significant applications of this result will be reviewed in the talk\, pa
 rticularly in connection to the Chow stability of the manifold\, and the n
 umerical computation of the Calabi-Yau metrics.\nOn the other hand\, examp
 les were found to show that the above theory does not carry over naively t
 o the case when the automorphism group is non-discrete. In this talk\, we 
 propose a new “quantising” equation\, which generalises various key re
 sults in Donaldson's quantisation when the automorphism group is no longer
  discrete\, and can be applied more generally to extremal Kähler metrics.
 \n\nhttp://www.homepages.ucl.ac.uk/~ucahyha/\nhttps://sites.google.com/vie
 w/yhashimoto/home
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Yoshinori_Hashimoto.jpg
CATEGORIES:Groupe de travail,Métriques à courbure spéciale
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DTSTART:20170326T030000
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