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In this Symplectic Geometry Seminar talk, explore the challenges of counting special Lagrangians in Calabi-Yau 3-folds and Fueter sections to define new numerical and Floer-theoretic invariants. Speaker Saman Habibi Esfahani from Duke University presents joint work with Yang Li, addressing key non-compactness problems and wall-crossing phenomena in these mathematical structures. Learn about Donaldson-Segal's proposed weighted count of special Lagrangians, where the weight is determined by counting Fueter sections. Discover the speaker's breakthrough compactness theorem for Fueter sections, addressing an open problem first raised by Taubes in 1998 that was motivated by defining new invariants of 3-manifolds. The presentation also covers a local version of the Donaldson-Scaduto conjecture, which is expected to be crucial for proving compactness results for special Lagrangians in Lefschetz-fibered Calabi-Yau 3-folds.
