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Explore a thought-provoking lecture on Hilbert spaces without the axiom of choice, delivered by Iljas Farah from York University as part of the 2022-2023 Set Theory Seminar at the Fields Institute. Delve into the intricacies of mathematical set theory and its implications for Hilbert spaces in this 97-minute presentation. Gain insights into the challenges and consequences of working with these mathematical structures in the absence of the axiom of choice, a fundamental principle in set theory. Expand your understanding of advanced mathematical concepts and their applications in this engaging seminar talk.