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Explore the theory of minimal modular extensions of braided fusion categories through this 55-minute mathematical seminar from the BIMSA-Tsinghua Quantum Symmetry Seminar series. Delve into the non-Tannakian (super-Tannakian) case as Professor César Galindo from Universidad de los Andes reviews Müger's notion of minimal modular extensions and presents an obstruction theory for determining when such extensions exist. Learn about the concrete obstruction in H^4(G,C^*) for the Tannakian case and discover the complete cohomological obstruction theory developed for the super-Tannakian setting. Examine the introduction of categorical fermionic actions, which generalize group actions to super-groups acting on fermionic fusion categories, enabling classification of minimal modular extensions in the super-Tannakian context and revealing new phenomena absent from classical cases. Understand how these results complement recent work by Johnson-Freyd and Reutter on slightly degenerate categories and contribute to the broader program of classifying modular categories via their minimal extensions, with applications to quantum computing and representation theory of quantum groups.
