Complete Calabi-Yau metrics and optimal transport problems

Abstract: Calabi-Yau metrics are Ricci-flat and K\"ahler metrics and they are a central part of K\"ahler geometry. The construction of Calabi-Yau metrics on compact K\"ahler manifolds has been understood since Yau's resolution of the Calabi conjecture. By contrast, the situation in the complete non-compact case is much more intricate and remains an active area of research. In this talk, I will discuss some recent developments in the study of complete Calabi-Yau metrics where the regularity theory of an optimal transport problem plays a big role. This is based on joint work with Tristan Collins and Shing-Tung Yau.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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