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Explore an innovative mathematical approach to characteristic subgroups that breaks free from the traditional circular dependence on automorphisms in this 54-minute conference talk. Learn how characteristic subgroups, classically defined through invariance under group automorphisms, create a computational paradox when neither the automorphisms nor the characteristic subgroups are initially known. Discover a groundbreaking impredicative definition of characteristic structure based on representation theory of the category of groups, which provides a pathway to establish these fundamental mathematical objects without prior knowledge of automorphisms. Examine the practical implications of this theoretical breakthrough for certified computation in group theory, including computational methods and verification processes. Gain insights into collaborative research that bridges abstract algebra and computational mathematics, presenting solutions to longstanding problems in algorithmic group theory and automated theorem proving.
