Harmonic Maps and Rigidity
Offered By: Fields Institute via YouTube
Course Description
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
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