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UID:ad0e6d9d4615198aea347120ec1c95f5
CATEGORIES:Joint Princeton-Rutgers Seminar on Geometric PDE's
CREATED:20221128T101450
SUMMARY:Collapsing Ricci-flat metrics: estimates or no estimates?
LOCATION:Fine Hall 110\, Princeton University
DESCRIPTION:Abstract: Compact Calabi-Yau manifolds admit Ricci-flat Kahler metrics than
 ks to a celebrated theorem of Yau, a unique such metric in each Kahler coho
 mology class. If we degenerate the class, the corresponding Ricci-flat metr
 ics will also degenerate, and one can ask whether they admit uniform bounds
  (in all C^k norms) away from a closed analytic subvariety. This is known w
 hen the metrics are not collapsing, but the collapsing case is much more ch
 allenging. I will discuss how the answer to this question is positive when 
 the limiting class comes from the base of a fibration (joint with Hein), an
 d negative in general when there is no such fibration (joint with Filip), a
 nd raise some related open questions.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract:&nbsp;</strong>Compact Calabi-Yau manifolds admit Ricci
 -flat Kahler metrics thanks to a celebrated theorem of Yau, a unique such m
 etric in each Kahler cohomology class. If we degenerate the class, the corr
 esponding Ricci-flat metrics will also degenerate, and one can ask whether 
 they admit uniform bounds (in all C^k norms) away from a closed analytic su
 bvariety. This is known when the metrics are not collapsing, but the collap
 sing case is much more challenging. I will discuss how the answer to this q
 uestion is positive when the limiting class comes from the base of a fibrat
 ion (joint with Hein), and negative in general when there is no such fibrat
 ion (joint with Filip), and raise some related open questions.</p>
CONTACT:Valentino Tosatti, Courant Institute, NYU
DTSTAMP:20260830T130048
DTSTART;TZID=America/New_York:20221209T143000
DTEND;TZID=America/New_York:20221209T153000
SEQUENCE:0
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