Speaker
Sohaib Khalid, Umeå University
Abstract
Recent works of Y. Li show that the weak metric SYZ conjecture holds for maximally degenerate families of Calabi-Yau manifolds. The proof crucially uses the existence of valuatively independent bases (recently established by work of Blum-Liu) for powers of the polarising line bundle to construct a cost function for an optimal transport problem. In order to better understand the regularity of the corresponding special Lagrangian torus fibration, a more explicit description of this ‘valuative’ cost function is arguably required. In this talk, we will explicitly describe the valuative cost function in a specific example, obtained by an explicit construction of a sequence of valuatively independent bases. Following this, we will motivate a general proposal for a canonical cost function using the monodromy of an affine structure on the essential skeleton. This is joint work with Jakob Hultgren.