BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Abdellah Lahdili (UQAM)
DTSTART:20231020T150000Z
DTEND:20231020T161500Z
DTSTAMP:20260423T021354Z
UID:CIRGET/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/106/"
 >The Einstein-Hilbert functional in Kähler and Sasaki geometry</a>\nby Ab
 dellah Lahdili (UQAM) as part of CRM - Séminaire du CIRGET / Géométrie 
 et Topologie\n\nLecture held in PK-5115.\n\nAbstract\nGiven a polarised K\
 \"ahler manifold $(M\,L)$\, we consider the circle bundle associated to th
 e polarization with the induced transversal holomorphic structure. The spa
 ce of contact structures compatible with this transversal structure is nat
 urally identified with a bundle\, of infinite rank\, over the space of K\\
 "ahler metrics in the first Chern class of $L$. We show that the Einstein-
 -Hilbert functional of the associated Tanaka--Webster connections is a fun
 ctional on this bundle\, whose critical points are constant scalar curvatu
 re Sasaki structures. In particular\, when the group of automorphisms of $
 (M\,L)$ is discrete\, these critical points correspond to constant scalar 
 curvature K\\"ahler metrics in the first Chern class of $L$. We show that 
 the Einstein--Hilbert functional satisfies some monotonicity properties al
 ong some one-parameter families of CR-contact structures that are naturall
 y associated to test configurations\, and that its limit on the central fi
 ber 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 polariz
 ed manifold implies K-semistability. This is a joint work with Eveline Leg
 endre and Carlo Scarpa.\n
LOCATION:https://researchseminars.org/talk/CIRGET/106/
END:VEVENT
END:VCALENDAR