BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yury Ustinovskiy (New York University) DTSTART:20210412T150000Z DTEND:20210412T160000Z DTSTAMP:20260423T052956Z UID:DGSTO/13 DESCRIPTION:Title: G ibbons-Hawking ansatz and Generalized Kahler solitons\nby Yury Ustinov skiy (New York University) as part of Differential Geometry Seminar Torino \n\n\nAbstract\nIn the last decades geometric flows have been proved to be a powerful tool in the classification and uniformization problems in geom etry and topology. Despite the wide range of applicability of the existing analytical methods\, we are still lacking efficient tools adapted to the study of general (non-Kahler) complex manifolds. In my talk I will discuss the pluriclosed flow - a modification of the Ricci flow - which was intro duced by Streets and Tian\, and shares many nice features of the Ricci flo w. The important open questions driving the ongoing research in complex ge ometry are the classification of compact non-Kahler surfaces\, and the Glo bal Spherical Shell conjecture. Our hope is that understanding the long-ti me behaviour and singularities of the pluriclosed flow well enough\, we ca n use it to approach these open questions.\n\nTo apply an analytic flow to any geometric problem\, we need to make the first necessary step - classi fy the stationary points of the flow\, and\, more generally\, its solitons (stationary points modulo diffeomorphisms). For the pluriclosed flow\, th is question reduces to a non-linear elliptic PDE for an Hermitian metric o n a given complex manifold. We will discuss this problem on compact/comple te complex surfaces\, and provide exhaustive classification under natural extra geometric assumptions. In the course of our classification we will d iscover a natural extension of the famous Gibbons-Hawking ansatz for hyper Kahler manifolds.\n LOCATION:https://researchseminars.org/talk/DGSTO/13/ END:VEVENT END:VCALENDAR