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Harmonic Analysis

Monge-Ampere equations, stability, and asymptotics for energy functionals

speaker: Duong Phong (Columbia University)

abstract: We discuss the problem of finding Kähler-Einstein metrics on manifolds of positive first Chern class. This reduces to the solution of Monge-Ampere equations, whose existence has been conjectured by S.T. Yau to be equivalent to stability in the sense of geometric invariant theory. We discuss the relation of stability to energy functionals, and the exact evaluation of these for complete intersections.

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