GT seminar: "Singular Lagrangian Torus Fibrations on the smoothing of algebraic cones"

Abstract: In this talk, we explore a new approach to special Lagrangian fibrations on the smoothing of Gorenstein singularities, initially introduced by Gross and further analyzed in the context of the SYZ conjecture of mirror symmetry. Utilizing global coordinates connected to Altmann's characterization of the smoothing, our methodology not only provides alternative proofs for existing theorems about these fibrations but also expands on Symington’s work by creating a convex base diagram in higher dimensions. Additionally, we apply techniques from Pascaleff and Tonkonog to recover Lau's calculation of the potential for certain monotone fibers and investigate the non-displaceability of these fibers. This presentation includes a series of illustrative examples and concludes with an overview of future research directions.

This is a talk in our Geometry and Topology seminar series.