CORDIS Project
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This project introduces a new probabilistic method to study Kähler-Einstein metrics on complex manifolds, linking algebraic and differential geometry. It aims to establish conditions for the existence of these metrics through a novel statistical mechanical approach.
In broad terms the aim of this proposal is to introduce a new probabilistic approach to the study of Kähler-Einstein (K-E) metrics on complex manifolds.
A precise procedure, based on a blend of Statistical Mechanics, Pluripotential theory and Kähler Geometry. will be used to show that• when a K-E metric exists on a complex manifold X it can be obtained from the “largeN limit” of certain canonical random point processes on X with N particles.The canonical point processes are directly defined in…
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