Hopf Cyclic Cohomology

Explore Hopf cyclic cohomology in this 57-minute lecture by Masoud Khalkhali from Western University, delivered at the Fields Institute on September 28th, 2021, as part of the "Cyclic Cohomology at 40: achievements and future prospects" conference. Delve into topics such as deformation complex, Deligne's conjecture, Bar-Cobar duality, cyclic homology of Hopf crossed products, and the Connes-Moscovici breakthrough. Examine modular pairs in involution, stable anti-Yetter-Drinfeld modules, and Hopf cyclic cohomology with coefficients. Investigate the connections between braided monoidal categories, cyclic homology, and 2-traces. Gain insights into the historical development and future directions of this mathematical field, from the 1997 Portugal meeting to recent advancements in SAYD modules and cyclic homology with coefficients.