Lagrangian Torus Fibrations Over Affine Manifolds with Gross-Siebert Singularities

Explore a mathematical lecture from the University of Southampton's Cheuk Yu Mak examining the construction of Lagrangian torus fibrations on symplectic manifolds with prescribed integral affine bases with singularities, based on joint work with Diego Matessi, Helge Ruddat, and Ilia Zharkov. Delve into the construction of local models and their Lagrangian torus fibrations, focusing on two key features: the canonical 'pseudo-product' nature of Lagrangian torus fibration in regions with larger torus symmetry, and the relationship between local models and hypersurfaces inside toric varieties governed by potential functions. Learn how these features enable seamless transitions between different local model types without additional tori splitting choices, while allowing interpolation between auxiliary choices of same-type local models, culminating in an explanation of local model assembly through canonical slice selection from a canonical family.