BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Uwe Semmelmann (Universität Stuttgart) DTSTART:20210225T133000Z DTEND:20210225T143000Z DTSTAMP:20260423T024540Z UID:GeoSem/18 DESCRIPTION:Title: Stability of Einstein metrics\nby Uwe Semmelmann (Universität Stuttga rt) as part of Geometry Seminar - University of Florence\n\n\nAbstract\nEi nstein metrics can be characterised as critical points of\nthe (normalised ) total scalar curvature functional. They are always\nsaddle points. Howev er\, there are Einstein metrics which are local\nmaxima of the functional restricted to metrics of fixed\nvolume and constant scalar curvature. Thes e are by definition stable\nEinstein metrics. Stability can equivalently b e characterised by\na spectral condition for the Lichnerowicz Laplacian on divergence- and\ntrace-free symmetric 2-tensors\, i.e. on so-called tt-te nsors:\nan Einstein metric is stable if twice the Einstein constant is a l ower\nbound for this operator. Stability is also related to Perelman's\n\\ nu entropy and dynamical stability with respect to the Ricci flow.\n\nIn m y talk I will discuss the stability condition. I will present a\nrecent re sult obtained with G. Weingart\, which completes the work\nof Koiso on the classification of stable compact symmetric spaces.\nMoreover\, I will des cribe an interesting relation between instability\nand the existence of ha rmonic forms. This is done in the case of nearly\nKähler\, Einstein-Sasa ki and nearly G_2 manifolds. If\ntime permits I will also explain the inst ability of the Berger space\nSO(5)/SO(3)\, which is a homology sphere. In this case\ninstability surprisingly is related to the existence of Killing tensors.\nThe latter results are contained in joint work with\nM. Wang an d C. Wang.\n LOCATION:https://researchseminars.org/talk/GeoSem/18/ END:VEVENT END:VCALENDAR