Introduction to canonical metrics and stability notions in Kahler geometry14

Title: Introduction to canonical metrics and stability notions in Kahler geometry14 

Time & Venue: 2022, June 25th(Saturday) 14:00-15:30 Tencent：71630366211. 

Abstract: In this series of lectures we will review the basic ideas surrounding the so called Yau-Tian-Donaldson conjecture, whose goal is to search for canonical metrics on Kahler manifolds. On the analytic side we will recall basic pluripotential theory and then introduce notions such as K-energy, Ding energy, Bergman kernels etc. On the algebraic side, we shall explain notions such as K-stability, Ding stability, filtrations, valuations, Okounkov bodies, stability thresholds etc. A good reference for this lecture series would be the paper "Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs" by Boucksom-Hisamoto-Jonsson.