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Explore the construction of enumerative invariants from general Calabi-Yau categories in this 44-minute mathematical physics lecture. Delve into Kontsevich's homological mirror symmetry proposal from 1994 and learn how to recover Gromov-Witten invariants from the Fukaya category of a symplectic manifold. Examine the construction of invariants associated with general Calabi-Yau categories following the work of Costello and Caldararu-T., which conjecturally generalize Gromov-Witten invariants, Fan-Jarvis-Ruan-Witten invariants, and Saito-Givental invariants simultaneously. Discover how these invariants, when applied to the derived category of coherent sheaves of a smooth projective Calabi-Yau, should conjecturally match with BCOV invariants in string theory. Survey recent progress in this rapidly developing field at the intersection of algebraic geometry, symplectic geometry, and mathematical physics.
