BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Diego Conti (Università di Pisa) DTSTART:20260923T160000Z DTEND:20260923T170000Z DTSTAMP:20260914T071132Z UID:VSGS/140 DESCRIPTION:Title: H omogeneous metrics and spinors\nby Diego Conti (Università di Pisa) a s part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nOn a Riemannian manifold\, the existence of a Killing spinor forces the metric to be Einstein. The homogeneous picture is completely understood\; for neg ative scalar curvature only hyperbolic space occurs\, whilst positive scal ar curvature contains several examples\, in particular the flag manifold $ U(3)/T^3$ and the Sasaki quotients $U(n)/T^{n-1}$\, themselves fibering ov er a flag manifold. For $n>3$\, the quotient $U(n)/T^n$ has no Killing spi nors\, but the Dirac operator for the normal metric acts in a remarkably s imple way on the space of invariant spinors\, which can be described in a purely combinatorial way.\n\nOn pseudo-Riemannian manifolds\, more homogen eous metrics with a Killing spinor appear. Through the lens of the Böhm-L afuente theorem and the Heber-Lauret theory of standard solvmanifolds\, th is greater flexibility appears as a consequence of the failure of the Iwas awa condition\, that lies at the heart of the correspondence between Einst ein solvmanifolds and nilsolitons in positive-definite signature. I will s how how imposing this condition recovers the same rigidity\, and\, by cont rast\, a construction that produces Einstein solvmanifolds not extending a nilsoliton that carry Killing spinors.\n\nThe talk will touch joint proje cts with F. A. Rossi and R. Segnan and with S. Salamon.\n LOCATION:https://researchseminars.org/talk/VSGS/140/ END:VEVENT END:VCALENDAR