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Delve into the fourth lecture of a graduate-level course on K-Theory and C*-Algebras, presented by renowned instructor George Elliott from the University of Toronto. Explore advanced concepts in operator algebras and their applications as part of the Fields Institute's Thematic Program on Operator Algebras and Applications. Gain insights into complex mathematical theories and their practical implications in this 53-minute session, recorded on September 15, 2023. Enhance your understanding of operator K-theory and its connections to C*-algebras, building upon the foundations laid in previous lectures. Engage with cutting-edge research and theoretical frameworks in this specialized field of mathematics.