Given a family (X_t) of complex Calabi-Yau manifolds, the SYZ conjecture concerns the geometric structure of the fibers X_t, as t goes to 0 and the complex structure of X_t degenerates in the worst possible way. Kontsevich and Soibelman introduced a non-archimedean approach to this conjecture, and more recently, Yang Li’s work has connected the non-archimedean approach with the original SYZ conjecture.

In this talk, I will explain the key concepts of the non-archimedean approach and present recent developments in the context of hypersurfaces. This is based on a project in collaboration with Jakob Hultgren, Mattias Jonsson and Nick McCleerey.