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Math-Physics Joint Seminar

Tuesday, November 5, 2019 - 4:30pm

Sara Tukachinsky



University of Pennsylvania

DRL 4c2

In a joint work with Jake Solomon, we used Fukaya A_\infty algebras and  bounding chains to define genus zero open Gromov-Witten invariants. These invariants count configurations of pseudoholomorphic disks in a symplectic manifold X with boundary conditions in a Lagrangian submanifold L. However, the construction is rather abstract. Nonetheless, in recent work with Jake Solomon, we find that the superpotential that generates these invariants has many properties that enable calculations. Most notably, the superpotential satisfies the open Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. For (X,L)=(CP^n,RP^n), the open WDVV give rise to recursion relations that allow the computation of all invariants. Furthermore, the open WDVV can be reinterpreted as the associativity of a quantum product on relative cohomology H^*(X,L).