BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David González Álvaro (Universidad Politécnica de Madrid) DTSTART:20260527T160000Z DTEND:20260527T170000Z DTSTAMP:20260513T203848Z UID:VSGS/129 DESCRIPTION:Title: R icci flow preserves positive curvature on homogeneous spheres\nby Davi d González Álvaro (Universidad Politécnica de Madrid) as part of Virtua l seminar on geometry with symmetries\n\n\nAbstract\nSince Hamilton introd uced the Ricci flow in 1982\, it has been a fundamental question to unders tand which curvature conditions are preserved under the flow. In this talk we focus on the notion of positive sectional curvature\, denoted sec>0. H amilton proved that sec>0 is preserved in dimensions 2 and 3. In contrast\ , there are examples of manifolds in dimensions 4\, 6\, 7\, 12\, 13 and 24 where sec>0 is not preserved. In the search of new examples it is natural to look at homogeneous manifolds. In this work we prove that spheres do n ot provide new examples\, i.e. the flow preserves sec>0 on homogeneous sph eres. We also show that the same holds for all compact rank one symmetric spaces. Together with previous works\, this classifies simply connected ma nifolds which admit a homogeneous metric for which sec>0 is not preserved under the flow. This is joint work with Jason DeVito and Masoumeh Zarei.\n LOCATION:https://researchseminars.org/talk/VSGS/129/ END:VEVENT END:VCALENDAR