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SUMMARY:BASIC NOTIONS SEMINAR: The Calabi Problem
DTSTART;VALUE=DATE-TIME:20260116T100000Z
DTEND;VALUE=DATE-TIME:20260116T110000Z
DTSTAMP;VALUE=DATE-TIME:20260419T021654Z
UID:indico-event-11252@ictp.it
DESCRIPTION:\n	Abstract\n	In his 1954 ICM lecture\, Eugenio Calabi popular
 ized a formidable problem at the confluence of differential and algebraic 
 geometry\, which became known as the Calabi problem. The problem asks whic
 h compact complex manifolds admit a special type of constant-curvature met
 ric\, known as a Kähler-Einstein metric.\n	For Kähler manifolds with eit
 her flat or negative curvature\, the Calabi problem was solved in the 1970
 s by Yau and by Aubin and Yau. They confirmed Calabi’s prediction\, show
 ing that such manifolds always admit a Kähler-Einstein metric. However\, 
 in the case of positively curved projective manifolds - known as Fano mani
 folds - the existence of a Kähler-Einstein metric is not guaranteed.\n	In
  the past decade\, surprising and deep connections have emerged between th
 e existence of Kähler-Einstein metrics and birational geometry\, leading 
 to significant advances in the Calabi problem. In this talk\, I will discu
 ss the problem itself\, its links with birational geometry\, and the curre
 nt state of the art in dimension three.\n\n//indico.ictp.it/event/11252/
LOCATION:ICTP Leonardo Building - Luigi Stasi Seminar Room
URL://indico.ictp.it/event/11252/
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