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Explore the fascinating world of N=1 SVOAs and their connections to exceptional finite groups in this 58-minute lecture by Theo Johnson-Freyd at the Centre de recherches mathématiques (CRM). Delve into a two-part presentation that first tackles the classification of N=1 SVOAs with specific natural properties and their automorphism groups. Discover two infinite families related to alternating groups and eleven exceptions linked to the "Suzuki chain" of exceptional subgroups within Conway's largest sporadic group. Examine the implementation of a "level-rank duality" inside the Conway Moonshine SCFT, which connects the Suzuki chain to a chain of alternating subgroups. In the second half, investigate various constructions involving duality, gauging, and coset models. Consider the possibility of an intriguing family of SVOAs related to the Mathieu groups and their potential duality to actions of SU(2)l fusion categories on the Conway Moonshine SCFT. Gain insights into quantum symmetries, tensor categories, topological quantum field theories, and vertex algebras through this advanced mathematical exploration.
