Topology Seminar

Date: March 2, 2022

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Mohan Swaminathan, Princeton University

Title: Towards an extension of Taubes' Gromov invariant to Calabi--Yau 3-folds

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.