BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alejandro Tolcachier (CIEM-CONICET) DTSTART:20260703T170000Z DTEND:20260703T180000Z DTSTAMP:20260924T102358Z UID:AmSurAmSulGeometry/111 DESCRIPTION:Title: Linear stability of Perelman's $\\nu$-entropy functional on s tandard Einstein manifolds\nby Alejandro Tolcachier (CIEM-CONICET) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nRecently\, Paul Schwa hn showed that\, contrary to previous expectations\, there exist many comp act\, simply connected standard Einstein manifolds that are not symmetric spaces and are stable with respect to the total scalar curvature functiona l restricted to the space of Riemannian metrics with constant scalar curva ture and fixed volume. This stability follows from the inequality $\\lambd a_L>2E$\, where $\\lambda_L$ denotes the smallest eigenvalue of the Lichne rowicz Laplacian restricted to $TT$-tensors\, and $E$ is the Einstein cons tant.\n\nIn this talk\, we will see how Lie-theoretic methods can be used to estimate the first positive eigenvalue $\\lambda_1$ of the Laplace-Belt rami operator on compact\, simply connected non-symmetric standard Einstei n manifolds $(G/H\,g_{st})$\, where $G$ is a compact\, connected\, simple Lie group. Our main result shows that $\\lambda_1>2E$ for all such manifol ds\, with only seven exceptions.\n\nThese estimates imply that all the Ein stein manifolds proved stable by Schwahn are\, in fact\, linearly stable w ith respect to Perelman's $\\nu$-entropy functional. This complements prev ious work of Cao and He on compact irreducible symmetric spaces.\n\nThis t alk is based on joint work with Emilio Lauret (Universidad Nacional del Su r\, Argentina).\n LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/111/ END:VEVENT END:VCALENDAR