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Geometric Analysis Seminar

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

Mohan Swaminathan (Princeton University)

Location:  Zoom
Date & time: Tuesday, 08 February 2022 at 2:50PM - 3:50PM

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.

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