Explore a comprehensive lecture on conformal field theory (CFT) correlators using a skein theoretic approach. Delve into complex CFT, double mapping class groups, and orientation in local coordinates. Examine complex geometry, structures, and manifolds, as well as simple connectivity and fundamental domains. Investigate classical results, vertex algebras, and the Virasoro algebra, including eigenvalues and super extensions. Gain insights into algebraic structures and their applications in CFT. This in-depth presentation, delivered by Christoph Schweigert at the Galileo Galilei Institute, offers a thorough exploration of advanced topics in theoretical physics and mathematics over the course of nearly two hours.