Explore the intricacies of representation theory in this comprehensive lecture on the deformation of representation and fusion rings for Lie algebras. Delve into advanced mathematical concepts as Swarnava Mukhopadhyay presents cutting-edge research in the field of algebraic and combinatorial methods in representation theory. Gain insights into the connections between infinite-dimensional Lie (super)algebras, quantum groups, and vertex algebras, and their applications in mathematics and physics. Discover how these complex theories intersect with other areas of study and contribute to solving outstanding problems in the field. Suitable for graduate students, postdoctoral scholars, and researchers interested in expanding their knowledge of modern representation theory and Lie theory.