| 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. |
