Symplectic Geometry Seminar

This talk is based on joint work with Yang Li. I will discuss the problem of counting special Lagrangians in Calabi-Yau 3-folds and Fueter sections to define new numerical and Floer-theoretic invariants. The key challenges are the non-compactness problems and the wall-crossing phenomenon. Donaldson-Segal proposed a weighted count of special Lagrangians to remedy this problem, where the weight is determined by counting Fueter sections. However, the compactness of the space of Fueter sections is an open problem, first raised by Taubes in 1998, motivated by defining new invariants of 3-manifolds. In this work, we prove a compactness theorem for Fueter sections and also, if time permits, a local version of the Donaldson-Scaduto conjecture. This conjecture is expected to play a major role in proving compactness results for special Lagrangians in Lefschetz-fibered Calabi-Yau 3-folds.