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SUMMARY:Song Sun (University of California\, Berkeley)
DTSTART:20230328T150000Z
DTEND:20230328T160000Z
DTSTAMP:20260423T022721Z
UID:Geolis/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/116/"
 >Complete Calabi-Yau metrics asymptotic to cones</a>\nby Song Sun (Univers
 ity of California\, Berkeley) as part of Geometria em Lisboa (IST)\n\n\nAb
 stract\nComplete Calabi-Yau metrics provide singularity models for limits 
 of Kahler-Einstein metrics. We study complete Calabi-Yau metrics with Eucl
 idean volume growth and quadratic curvature decay. It is known that under 
 these assumptions the metric is always asymptotic to a unique cone at infi
 nity. Previous work of Donaldson-S. gives a 2-step degeneration to the con
 e in the algebro-geometric sense\, via a possible intermediate object (a K
 -semistable cone). We will show that such intermediate K-semistable cone d
 oes not occur. This is in sharp contrast to the case of local singularitie
 s. This result together with the work of Conlon-Hein also give a complete 
 algebro-geometric classification of these metrics\, which in particular co
 nfirms Yau’s compactification conjecture in this setting. I will explain
  the proof in this talk\, and if time permits I will describe a conjectura
 l picture in general when the curvature decay condition is removed. Based 
 on joint work with Junsheng Zhang (UC Berkeley).\n
LOCATION:https://researchseminars.org/talk/Geolis/116/
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