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SUMMARY:Stable maps in higher dimensions
DTSTART:20180417T134500
DTEND:20180417T144500
DTSTAMP:20260406T211414Z
UID:3cc838d89b0e96b409ff50f709a496bc18d77b639a031517bf14f4d9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ruadhai Dervan (University of Cambridge)\nOne of the basic que
 stions in complex geometry is to understand the existence of certain canon
 ical Kähler metrics on smooth complex manifolds or projective varieties. 
 On Riemann surfaces one can ask for metrics of constant curvature\, of pre
 scribed curvature more generally\, or of constant curvature but with presc
 ribed singularities at points. In higher dimensions the correct analogue o
 f constant curvature metrics are constant scalar curvature Kähler metrics
 \, an important special case being Kähler-Einstein metrics. I will discus
 s the Yau-Tian-Donaldson conjecture\, which relates the existence of these
  metrics to an algebro-geometric notion called K-stability. I will then di
 scuss an extension of these ideas to the setting of maps between complex m
 anifolds. On the algebraic notion this leads to a notion of stability whic
 h generalises Kontsevich's definition for Riemann surfaces\, while on the 
 analytic side the canonical Kähler metrics are analogous to metrics with 
 prescribed curvature on Riemann surfaces. This is joint work with Julius R
 oss.
LOCATION:MA A1 12 https://plan.epfl.ch/?room=MAA110
STATUS:CONFIRMED
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