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UID:f742288780e8a18264daa7f4115001cb
CATEGORIES:Gauge Theory Learning Seminar
CREATED:20260415T192836
SUMMARY:Einstein metrics from Derdziński duality
LOCATION:Hill 705 and Zoom
DESCRIPTION:<p><span data-olk-copy-source="MessageBody">Abstract</span>: (joint work wi
 th Rosa Sena-Dias) A theorem of Derdziński from the 1980's establishes that
  certain Einstein metrics are conformal to Bach-flat extremal Kahler metric
 s. Using this result, Rosa Sena-Dias and I classified conformally Kähler, U
 (2)-invariant, Einstein metrics on the total space of O(−m). This yields in
 finitely many 1-parameter families of metrics exhibiting several different 
 behaviors, including asymptotically hyperbolic, ALF, and metrics that compa
 ctify to a Hirzebruch surface with a cone singularity along the "divisor at
  infinity." As an application of these results, some interesting phenomena 
 occur. For instance, we exhibit the Taub-bolt Ricci-flat ALF metric as a li
 mit of cone angle Einstein metrics on the blow-up of CP² at a point (in the
  limit when the cone angle converges to zero). We also construct asymptotic
 ally hyperbolic Einstein metrics that are&nbsp;conformal to a scalar-flat K
 ähler metric and cannot be obtained by applying Derdziński's theorem.&nbsp;
 </p>
CONTACT:Goncalo Oliveira (Instituto Superior Tecnico Lisbon)
DTSTAMP:20260826T094726
DTSTART;TZID=America/New_York:20260421T100000
DTEND;TZID=America/New_York:20260421T230000
SEQUENCE:0
TRANSP:OPAQUE
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