Explore a comprehensive lecture on harmonic maps and rigidity presented by Chikako Mese from Johns Hopkins University at the Fields Institute. Delve into topics such as harmonic maps between Riemannian manifolds, existence theory, Mostow and Margulis Rigidity, and Siu's Holomorphic Rigidity. Examine the differences between uniform and non-uniform lattices, and investigate non-compact domains. Learn about the Bochner method, infinite energy harmonic maps, and the proof of existence for such maps in various dimensions. Gain insights into Teichmüller theory, integral rigidity, and the fundamental group of quasi-projective varieties. This 51-minute talk, part of the Workshop on Geometry of Spaces with Upper and Lower Curvature Bounds, offers a deep dive into the mathematical concepts surrounding harmonic maps and their applications in rigidity theory.