Towards a symplectic Pandharipande–Thomas invariant

In 2007, Pandharipande–Thomas constructed an invariant for smooth projective Calabi–Yau 3–folds which counts stable pairs (roughly: curves with divisors).  The PT/GW conjecture predicts that their invariant is equivalent to the Gromov–Witten invariant.  It is therefore reasonably to expect that a symplectic analogue of the Pandharipande–Thomas invariant should exists.  The purpose of this talk is to sketch a proposal developed in joint work with Doan and discuss some of the progress obtained in joint work with Doan and Zhang.