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Explore advanced symplectic geometry through this specialized conference talk that demonstrates how quilted Floer cochain complexes form (A∞,n) modules over the Fukaya category Fuk(M×M⁻). Learn how the speaker proves that when restricting input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex can be identified with bar complex from ordinary Floer theory. Discover the application of this theoretical framework to prove two long exact sequences conjectured by Seidel, which relate the Lagrangian Floer cohomology of collections of potentially intersecting Lagrangian spheres Li and the fixed point Floer cohomology of composed Dehn twists τL1∘...∘τLn along them. This presentation, delivered as part of the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series, provides insight into cutting-edge research connecting quilted Floer theory, A∞ structures, and Dehn twist dynamics in symplectic topology.
