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Explore the fundamentals of the Cuntz semigroup in this 53-minute lecture delivered by Eduard Vilalta at the Fields Institute. Delve into the core concepts and applications of this mathematical structure within the field of operator algebras. Gain insights into how the Cuntz semigroup relates to broader topics in functional analysis and C*-algebras. Examine its role in the classification of C*-algebras and its connections to other important constructions in operator theory. Suitable for graduate students and researchers in mathematics, this talk provides a solid foundation for further study in operator algebras and their applications.