BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Patric Donovan (University of New South Wales) DTSTART:20251001T220000Z DTEND:20251001T230000Z DTSTAMP:20260423T021327Z UID:VSGS/118 DESCRIPTION:Title: B ubble sheets and $\\kappa$-solutions in four-dimensional Ricci flow\nb y Patric Donovan (University of New South Wales) as part of Virtual semina r on geometry with symmetries\n\n\nAbstract\nAs discovered by Perelman\, t he study of ancient Ricci flows which are $\\kappa$-noncollapsed is a cruc ial prerequisite to understanding the singularity behaviour of more genera l Ricci flows. In dimension three\, these so-called "$\\kappa$-solutions" have been fully classified through the groundbreaking work of Brendle\, Da skalopoulos\, and Šešum. Their classification result can be extended to higher dimensions\, but only for those Ricci flows that have uniformly pos itive isotropic curvature (PIC)\, as well as weakly-positive isotropic cur vature of the second type (PIC2)\; it appears the classification result fa ils with only minor modifications to the curvature assumption. Indeed\, wi th the alternative assumption of non-negative curvature operator\, a rich variety of new examples emerge\, as recently constructed by Buttsworth\, L ai\, and Haslhofer\; Haslhofer himself has conjectured that this list of n on-negatively curved $\\kappa$-solutions is now exhaustive in dimension fo ur. In this talk\, we will discuss some recent progress towards resolving Haslhofer's conjecture\, including a compactness result for non-negatively curved $\\kappa$-solutions in dimension four\, and a symmetry improvemen t result for bubble-sheet regions. This is joint work with Anusha Krishna n and Timothy Buttsworth.\n LOCATION:https://researchseminars.org/talk/VSGS/118/ END:VEVENT END:VCALENDAR