Watch a 37-minute mathematics lecture from Harvard CMSA's series on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry where Professor Cuipo Jiang from Shanghai explores cohomological varieties in vertex operator algebras. Learn about the definition and examination of cohomological variety in vertex algebra, understanding its relationship as a cohomological dual to associated variety and its role in measuring smoothness of associated schemes at vertex points. Discover the construction of closed subvarieties for rational affine vertex operator algebras derived from finite dimensional simple Lie algebras, and understand the determination of cohomological varieties in simple Virasoro vertex operator algebras. Explore findings that demonstrate how rational C2-cofinite vertex operator algebras, while having associated varieties that are simple points, can possess cohomological varieties of significant dimensional complexity.