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Explore advanced mathematical concepts in this 57-minute conference talk that delves into the intricate connections between quantum groups, q-deformed W-algebras, and cluster algebras. Learn how free field representations provide a powerful framework for understanding these sophisticated algebraic structures, with particular emphasis on the role of cluster algebras in bridging quantum group theory and deformed W-algebra constructions. Discover the mathematical techniques used to construct and analyze these representations, gaining insights into the deep relationships between quantum algebraic structures and their geometric interpretations. Examine the theoretical foundations and computational methods that enable the study of q-deformations in the context of modern mathematical physics and representation theory.
