Vincent Guedj (U. Toulouse)
Canonical Metrics and Kähler-Ricci Flow
(10 hours)

Online PhD course
Period: 6-20 April 2021
Department of Mathematics
University of Rome "Tor Vergata"

YouTube page

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


(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


Differential calculus and geometry, complex analysis of one variable.


[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