Valuative independence for Calabi–Yau varieties

From the perspective of the Gross–Siebert program, the mirror symmetry of a maximal degeneration of Calabi–Yau varieties is governed by certain canonical bases for the sections of the powers of an ample line bundle on the degeneration. It is expected that the pairing between the basis elements and valuations in the essential skeleton satisfies an independence condition, similar to the pairing between monomials and monomial valuations on a toric variety. In this talk, I will explain how tools from birational geometry and K-stability can be used to construct bases that fulfill this condition. This is joint work with Harold Blum.