Speaker: Prof. Ziming Ma，Southern University of Science and Technology

Title: Localizing quantum connection via relative symplectic cohomology

Language: Chinese

Time & Venue: 2026.04.02 10:30-11:30 Zoom ID: 3329836068 Password: mcm1234

Abstract: In complex geometry, the Gauss-Manin connection for a family $X$ over $S$ can be described by the sheaf $\Omega^*_{X/S}$ of holomorphic de Rham forms. Motivated by mirror symmetry, we look for an A-model analogue using the framework of relative symplectic cohomology developed by U. Varolgunes. Taking a pre-quantum line bundle $L = O(D)$ over $M$ whose curvature is the symplectic form with fiberwise $S^1$ action, we consider the $S^1$-equivariant Hamiltonian Floer theory on the dual $L^*$ which comes with a Floer Gysin sequence. We construct a chain homotopy between the Floer-theoretic quantum connection, defined as in the work of P. Seidel and D. Pomerleano, and the connecting homomorphism of the Gysin sequence. Afterwards, we can define a relative Floer Gysin sequence on $L^*$. This is a joint work in progress with C.Y. Mak, D. Pomerleano, and U. Varolgunes.