Operations on Cyclic Complexes, Getzler-Gauss-Manin Connection, Noncommutative Crystalline Cohomology

Explore a 54-minute lecture on advanced mathematical concepts delivered by Boris Tsygan from Northwestern University. Delve into recent developments in algebraic operations on negative cyclic complexes and their applications. Discover how these operations facilitate the construction of Getzler's Gauss-Manin superconnection and the noncommutative crystalline complex of associative algebras. Gain insights into the work of Petrov-Vologodsky and Tsygan himself, focusing on operations on cyclic complexes, the Getzler-Gauss-Manin connection, and noncommutative crystalline cohomology.