Explore principal differential calculi on quantum flag manifolds in this comprehensive lecture by Thomas Weber from Università di Torino, Italy. Delve into key topics including introduction, examples, Graph Schneider Theorem, differential particle line, base and horizontal forms, principal covariant calculi, and proofs. Gain insights into advanced mathematical concepts and their applications in quantum geometry over the course of this 1-hour and 12-minute presentation at the Banach Center.