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Ruan-Tian deformations of the Cauchy-Riemann operator enable a geometric definition of (standard) Gromov-Witten invariants of semi-positive symplectic manifolds in arbitrary genera. We describe an analogue of these deformations compatible with our recent construction of real Gromov-Witten invariants in arbitrary genera. Our approach avoids the need for an embedding of the universal curve into a smooth manifold and systematizes the deformation-obstruction setup behind constructions of Gromov-Witten invariants.
Following a question of K. Hori at K. Fukayas 60th birthday conference, we relate the recently established WDVV-type relations for real Gromov-Witten invariants to topological recursion relations in a real setting. We also describe precisely the conn
We establish a system of PDE, called open WDVV, that constrains the bulk-deformed superpotential and associated open Gromov-Witten invariants of a Lagrangian submanifold $L subset X$ with a bounding chain. Simultaneously, we define the quantum cohomo
We use local Hamiltonian torus actions to degenerate a symplectic manifold to a normal crossings symplectic variety in a smooth one-parameter family. This construction, motivated in part by the Gross-Siebert and B. Parkers programs, contains a multif
We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the
Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya $A_infty$ endomorphism algebra of such a Lagrangian is quasi-isomorphic to