The non-archimedean SYZ fibration, I

This talk is based on joint work with Chenyang Xu and Tony Yue Yu. I will explain the construction of the non-archimedean Strominger–Yau–Zaslow fibration, whose existence was conjectured by Kontsevich and Soibelman in their non-archimedean approach to Mirror Symmetry. I will also explain why it is an affinoid torus fibration away from a codimension two subset of the base, as predicted by Kontsevich and Soibelman. The proof relies heavily on the Minimal Model Program in birational geometry.