Overview
Syllabus
Intro
Harmonic maps between Riemannian manifolds
Harmonic maps into CAT(0) spaces
Existence theory of harmonic maps
Mostow and Margulis Rigidity
Mostow's strong rigidity - geometric version
Harmonic maps approach to Rigidity
Siu's Holomorphic Rigidity
Mok-Siu-Yeung's Geometric Rigidity
Uniform lattice vs. Non-uniform lattice
Non-compact domains
Idea of the proof
The Bochner method
Existence of harmonic map for the compact case
Infinite energy harmonic maps in dime=1
Proof of existence of infinite energy maps
Proof in dimensions 2
Sketch of the existence of harmonic map
Sketch of the proof of pluriharmonicity
Proof in higher dimensions
Teichmüller theory
Integral rigidity
Fundamental group of a quasi-projective variety
Taught by
Fields Institute