Abstract
These lectures aim to provide an introduction to some recent developments in Kähler geometry.

Lectures

(1) Compact Kähler manifolds
• Examples, canonical metrics
• Quasi-plurisubharmonic functions

(2) Bounded Monge-Ampère measures
• Bedford-Taylor theory
• Uniform a priori estimates 

(3) Degenerate complex Monge-Ampère equations
• Finite-energy classes
• Variational approach 

(4) Singular Kähler-Einstein metrics
• Singular Calabi-Yau conjecture
• Mabuchi geometry of Q-Fano varieties

(5) The Kähler-Ricci flow
• Smooth minimal models
• Parabolic pluripotential theory

Prerequisites

Differential calculus and geometry, complex analysis of one variable.

References

    [1]  S. Boucksom & P. Eyssidieux & V. Guedj. An Introduction to the Kähler-Ricci Flow. Lecture Notes in Math. 2086, Springer (2013).
    [2]  J.-P. Demailly, Complex Analytic and Differential Geometry.
    [3]  V. Guedj & A. Zeriahi, Degenerate Complex Monge-Ampère Equations. EMS Tracts in Math. (2017), 496p.
     [4]  C. Voisin, Hodge Theory and Complex Algebraic Geometry. I. Cambridge University Press, Cambridge, 2002. x+322 pp