“This project delves into several research directions within representation theory, which is the mathematical framework for studying objects through their symmetries and the operations which preserve them. Such operations can carry a classical, or even more intriguingly a quantum algebraic structure. … Quantum groups and the theory surrounding them are now a thriving source of uncovering new mathematical principles. This project will develop a richer understanding of this theory by building a common ground for combining algebraic, combinatorial and higher-structural categorical techniques for the study of quantum groups and associated diagram algebras.”