BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eveline Legendre (U. Lyon) DTSTART:20231201T170000Z DTEND:20231201T180000Z DTSTAMP:20260502T095145Z UID:AmSurAmSulGeometry/68 DESCRIPTION:Title: The Einstein-Hilbert functional in Kähler and Sasaki geometry \nby Eveline Legendre (U. Lyon) as part of Geometry Webinar AmSur /AmS ul\n\n\nAbstract\nIn this talk I will present a recent joint work with Abd ellah Lahdilli and Carlo Scarpa where\, given a polarised Kähler manifold $(M\,L)$\, we consider the circle bundle associated to the polarization w ith the induced transversal holomorphic structure. The space of contact st ructures compatible with this transversal structure is naturally identifie d with a bundle\, of infinite rank\, over the space of Kähler metrics in the first Chern class of L. We show that the Einstein--Hilbert functional of the associated Tanaka--Webster connections is a functional on this bund le\, whose critical points are constant scalar curvature Sasaki structures . In particular\, when the group of automorphisms of $(M\,L)$ is discrete\ , these critical points correspond to constant scalar curvature Kähler me trics in the first Chern class of $L$. If time permits\, I will explain ho w we associate a two real parameters family of these contact structures to any ample test configuration and relate the limit\, on the central fibre\ , to a primitive of the Donaldson-Futaki invariant. As a by-product\, we s how that the existence of cscK metrics on a polarized manifold implies K-s emistability\n LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/68/ END:VEVENT END:VCALENDAR