The broad goal of this project is to uncover novel phenomena in Quantum Field Theory (QFT) at strong coupling. This project involves studying interesting examples of strongly interacting conformal and superconformal field theories in various dimensions (in particular, their local and non-local operators and associated algebras) as well as the renormalization group flows that connect them. The idea is to elucidate aspects of these theories that are not amenable to standard perturbative and non-perturbative analyses and also to uncover new algebraic, geometrical, and topological structures underlying QFT itself.