BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Hallam (Oxford University) DTSTART:20210219T160000Z DTEND:20210219T171500Z DTSTAMP:20260423T005733Z UID:CIRGET/32 DESCRIPTION:Title: Stability of fibrations through geodesic analysis\nby Michael Hallam ( Oxford University) as part of CRM - Séminaire du CIRGET / Géométrie et Topologie\n\n\nAbstract\nA celebrated result in geometry is the Kobayashi- -Hitchin correspondence\, which states that a holomorphic vector bundle on a compact Kähler manifold admits a Hermite--Einstein metric if and only if the bundle is slope polystable. Recently\, Dervan and Sektnan have conj ectured an analogue of this correspondence for fibrations whose fibres are compact Kähler manifolds admitting Kähler metrics of constant scalar cu rvature. Their conjecture is that such a fibration is polystable in a suit able sense\, if and only if it admits an optimal symplectic connection. In this talk\, I will provide an introduction to this theory\, and describe my recent work on the conjecture. Namely\, I show that existence of an opt imal symplectic connection implies polystability with respect to a large c lass of fibration degenerations. The techniques used involve analysing geo desics in the space of relatively Kähler metrics of fibrewise constant sc alar curvature\, and convexity of the log-norm functional in this setting. This is work for my PhD thesis\, supervised by Ruadhaí Dervan and France s Kirwan.\n LOCATION:https://researchseminars.org/talk/CIRGET/32/ END:VEVENT END:VCALENDAR