Seminars & Colloquia Calendar

Abstract: I will describe the construction of a virtual count of embedded pseudo-holomorphic curves of a given genus in a Calabi--Yau 3-fold lying in two times a primitive homology class. The result is an integer-valued symplectic deformation invariant which can be viewed as an analogue of Taubes' Gromov invariant (which is defined for symplectic 4-manifolds). The construction depends on a detailed bifurcation analysis of the moduli space of embedded curves along a generic path of almost complex structures and is partly motivated by Wendl's resolution of Bryan--Pandharipande's super-rigidity conjecture. This is based on joint work with Shaoyun Bai.