Speaker: Artan Sheshmani (BIMSA)
Abstract: We discuss construction of a derived Lagrangian intersection theory of closely related moduli spaces of perfect complexes, with support on divisors on compact Calabi Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We degenerate the CY3 into a normal-crossing singular variety composed of Fano threefolds meeting along their anti-canonical divisor. The derived Lagrangian intersection of the corresponding “Fano moduli spaces” provides one with categorification of DT invariants over the special fiber (of degenerating family). We then elaborate on the existence of a “Getzler-Gauss-Manin” connection on the Z/2-graded periodic cyclic homology associated to these categorified DT invariants. The latter provides the deformation invariance property, needed to relate the categorical DT invariants of the special fiber to the one over the generic fiber. If there is time, we also show how in terms of “non-derived” virtual interscetion theory these DT invariants relate to counts of D4-D2-D0 branes which are expected to have modularity property by the S-duality conjecture. This talk is based on joint work with Vladimir Baranovsky, Ludmil Katzarkov and Maxim Kontsevich.
Time: 16:00-19:00, Tuesday, October 8th, 2024
Location: Block A, No. 657 Songhu Road, Yangpu District, Shanghai
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