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UID:26696@https://evenements.uqam.ca
DTSTART:20231020T110000Z
SEQUENCE:10
TRANSP:OPAQUE
URL:https://evenements.uqam.ca/evenements/seminaire-du-cirget-the-einstein-
 hilbert-functional-in-kaehler-and-sasaki-geometry/26696?date=2023-10-20_11
 -00-00
LOCATION:UQAM - Pavillon Président-Kennedy (PK) (201\, avenue du Présiden
 t-Kennedy\, Montréal )
SUMMARY:Séminaire CIRGET: «The Einstein-Hilbert functional in Kähler and
  Sasaki geometry»
CLASS:PUBLIC
DESCRIPTION:Conférencier: Abdellah Lahdili\, UQAM\n\n\nRésumé: Given a p
 olarised Kähler manifold (M\,L)\, we consider the circle bundle associate
 d to the polarization with the induced transversal holomorphic structure. 
 The space of contact structures compatible with this transversal structure
  is naturally identified with a bundle\, of infinite rank\, over the space
  of Kähler metrics in the first Chern class of L. We show that the Einste
 in--Hilbert functional of the associated Tanaka--Webster connections is a 
 functional on this bundle\, whose critical points are constant scalar curv
 ature Sasaki structures. In particular\, when the group of automorphisms o
 f (M\,L) is discrete\, these critical points correspond to constant scalar
  curvature Kähler metrics in the first Chern class of L. We show that the
  Einstein--Hilbert functional satisfies some monotonicity properties along
  some one-parameter families of CR-contact structures that are naturally a
 ssociated to test configurations\, and that its limit on the central fiber
  of a test configuration is related to the Donaldson--Futaki invariant. As
  a by-product\, we show that the existence of cscK metrics on a polarized 
 manifold implies K-semistability. This is a joint work with Eveline Legend
 re and Carlo Scarpa.\n\n\n\nMot-clés : Géométrie\, Mathématiques\n\n
CATEGORIES:Séminaire
DTSTAMP:20260522T152005Z
CREATED:20231017T151549Z
LAST-MODIFIED:20231108T145843Z
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