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Explore a comprehensive lecture on the historical development of Ergodic Theory presented by renowned mathematician Yuval Peres at BIMSA. Trace the evolution of this mathematical field from its origins in Poincaré's recurrence phenomenon (1890) and Boltzman's ergodic hypothesis (1887) to modern applications. Learn how Von Neumann and Birkhoff established the ergodic theorem in 1932, and how Lévy applied it to continued fraction expansions. Discover the contributions of Kolmogorov, Sinai, and Ornstein in solving isomorphism problems using entropy concepts derived from Shannon's information theory. Understand the significance of Markov partitions developed by Adler, Weiss, Sinai, and Bowen as tools in smooth dynamics. Examine Kingman's subadditive ergodic theorem and its connections to probability theory, as well as Furstenberg's refinements of Poincaré recurrence and their links to combinatorial number theory. The 77-minute lecture, delivered by a Principal researcher at Microsoft, National Academy of Science member, and recipient of the Rollo Davidson and Loeve prizes, covers these breakthroughs and their modern developments, including the ergodic theory of group actions.
