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In this 53-minute lecture, Terence Tao presents a comprehensive survey on the delocalization of eigenvectors of random matrices, delivered as part of the Simons Collaboration on Localization of Waves annual meeting 2025. Explore the mathematical principles and recent developments in this specialized field of random matrix theory, as one of the world's leading mathematicians examines how eigenvectors distribute across matrices with random elements. The presentation covers fundamental concepts, research progress, and open problems related to eigenvector delocalization, providing valuable insights for researchers and mathematicians interested in random matrices and wave localization phenomena.
