BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shu-Cheng Chang (National Taiwan University) DTSTART:20230920T060000Z DTEND:20230920T070000Z DTSTAMP:20260423T052709Z UID:MAC8028/2 DESCRIPTION:Title: From Thurston Geometrization Conjecture to Mori Minimal Model Program\ nby Shu-Cheng Chang (National Taiwan University) as part of Trends in Math ematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nA ce ntral problem of differential geometry is the geometrization problem on ma nifolds. In particular\, it is to determine which manifolds admit certain geometric structures. One of methods is to understand and classify the sin gularity models of the corresponding nonlinear geometric evolution equatio n\, and to connect it to the existence problem of geometric structures on manifolds. \n In 1982\, R. Hamilton introduced the Ricci flow and then by studying the singularity models of Ricci flow\, G. Perelman completely solved Thurston geometrization conjecture and Poincare conjecture for a cl osed 3-manifold in 2002 and 2003.\n On the other hand\, Mori minimal mo del program in birational geometry can be viewed as the complex analogue o f Thurston's geometrization conjecture. In 1985\, H.-D. Cao introduced the Kähler-Ricci flow and then recaptured the Calabi-Yau Conjecture. Moreove r\, there is a conjecture picture by Song-Tian that the Kähler-Ricci flo w should carry out the analytic minimal model program with scaling on proj ective varieties. Recently\, Song-Weinkove established the above conjectur e on a projective algebraic surface. Furthermore\, via the Sasaki-Ricci fl ow\, Chang-Lin-Wu proved the Sasaki analogue of minimal model program on c losed quasi-regular Sasakian 5-manifolds.\n In this lecture\, I will add ress the above issues in some detail.\n LOCATION:https://researchseminars.org/talk/MAC8028/2/ END:VEVENT END:VCALENDAR