IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is Hamiltonian isotopic to a special Lagrangian section in this class if and only if a stability condition holds, in the sense of a slope inequality on objects in a set of exact triangles in the Fukaya-Seidel category. This agrees with general proposals by Li. Under more restrictive assumptions, this result can be used to show a precise relation with Bridgeland stability, as predicted by Joyce. Based on arXiv:2505.07228.