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Explore groundbreaking research in a seminar talk that delves into Lie theory within tensor categories and its applications to modular representation theory. Learn about innovative approaches to understanding tensor power decomposition of finite dimensional group representations in positive characteristic fields. Discover how new developments in Lie theory for tensor categories provide methods to prove the algebraicity of asymptotic multiplicities and derive explicit formulas for them. Follow along as the mathematical framework is developed to address long-standing questions about decomposition patterns of tensor powers, including bounds on the number of indecomposable summands of dimension coprime to characteristic p. Gain insights from joint work with K. Coulembier and V. Ostrik that establishes fundamental results about characters of Green rings and provides concrete bounds for asymptotic behavior. Access supplementary materials including detailed proofs in referenced papers and comprehensive slides that support the mathematical concepts presented in this advanced mathematical discourse.
