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Explore the fundamental principles of cyclic theory in this 59-minute lecture by renowned mathematician Alain Connes from IHES. Delivered at the Fields Institute on September 27, 2021, as part of the "Cyclic Cohomology at 40: achievements and future prospects" series, delve into the two essential backbones that form the foundation of cyclic theory. Gain insights into the historical development, current applications, and potential future directions of this mathematical concept, enhancing your understanding of its significance in modern mathematics and related fields.