SGGTC this Friday: Sara Tukachinsky
Oleg Lazarev
Dear all,
This Friday Sara Tukachinsky from IAS will give a talk at 1:00 pm in Math 520 (there will not be a lunch).
Best, Oleg
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Sara Tukachinsky: Open WDVV equations
Abstract: In a work from 2016, joint with Jake Solomon, we use 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. For instance, we establish a vanishing result that limits the amount of boundary constraints if L is homologically nontrivial. Other properties include a wall-crossing formula and open Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In fact, for (X,L)=(CP^n,RP^n), all possible values of the open Gromov-Witten invariants are computable by a recursive process. The open WDVV equations can be further reinterpreted as the associativity of a quantum product on relative cohomology H^*(X,L).
Abstract: In a work from 2016, joint with Jake Solomon, we use 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. For instance, we establish a vanishing result that limits the amount of boundary constraints if L is homologically nontrivial. Other properties include a wall-crossing formula and open Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In fact, for (X,L)=(CP^n,RP^n), all possible values of the open Gromov-Witten invariants are computable by a recursive process. The open WDVV equations can be further reinterpreted as the associativity of a quantum product on relative cohomology H^*(X,L).