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Explore a mathematical physics seminar presentation that delves into the construction of derived Lagrangian intersection theory for moduli spaces of perfect complexes on compact Calabi-Yau threefolds. Learn about deformation invariants associated with fixed linear systems of divisors in CY3, examining how Tyurin degeneration techniques break down Calabi-Yau threefolds into normal-crossing singular varieties composed of Fano threefolds. Discover how moduli spaces over Fano 4-fold demonstrate relative Lagrangian foliation structure, leading to their realization as derived critical loci of global (-1)-shifted potential functions. Understand the construction of flat Gauss-Manin connections and their role in relating periodic cyclic homology to derived Lagrangian intersections of Fano moduli spaces, ultimately contributing to the categorification of DT invariants. Examine the relationship between categorical DT invariants and D4-D2-D0 brane counting, including their expected modularity properties under S-duality conjecture.
