Explore noncommutative principal bundles on projective bases and their differential calculi in this 49-minute lecture by Paolo Aschieri from the University of Piemonte Orientale. Delivered on December 6, 2023, as part of the Workshop on Operator Algebras and Applications: Non-Commutative Geometry at the Fields Institute, this talk delves into advanced mathematical concepts within the framework of the Thematic Program on Operator Algebras and Applications. Gain insights into cutting-edge research in noncommutative geometry and its applications to operator algebras. For a detailed abstract and additional information about the workshop series, visit the provided links to the Fields Institute website.