BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jean-Pierre Bourguignon (IHÉS (Nicolaas Kuiper Honorary Professor )) DTSTART:20250625T140000Z DTEND:20250625T150000Z DTSTAMP:20260423T010636Z UID:GPL/48 DESCRIPTION:Title: Rev isiting the scalar curvature\nby Jean-Pierre Bourguignon (IHÉS (Nicol aas Kuiper Honorary Professor)) as part of Geometry and Physics @ Lisbon\n \nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThe sc alar curvature is the weakest invariant involving the curvature of a Riema nnian metric. On surfaces\, where the concept of curvature was first devel oped by Carl-Friedrich GAUSS\, the curvature reduces to it\, but in higher dimensions this scalar function misses a lot of information about the cur vature which is a 4-tensor field (it has 20 components in dimension 4). \n \nStill\, in the last 60 years problems connected to it have generated a h uge amount of literature because of an a priori totally unexpected deep i nterplay of the existence of a metric with positive scalar curvature with the topology of manifolds.\n\nThis has mobilised many radically new approa ches\, involving in particular spinors and a deeper understanding of a num ber of topological or differentiable invariants or constructions. \n\nTher e are still a number of open problems connected to prescribing the scalar curvature on a manifold\, and some will be presented.\n LOCATION:https://researchseminars.org/talk/GPL/48/ END:VEVENT END:VCALENDAR