TGiF-Seminar: Tropical geometry in Frankfurt (First meeting Summer Semester 2023)

Léonard Pille-Schneider (ENS, Paris)

Abstract: Let X -> D* be a polarized family of complex Calabi-Yau manifolds, whose complex structure degenerates in the worst possible way. The SYZ conjecture predicts that the fibers X_t, as t ->0, degenerate to a tropical object; and in particular the program of Kontsevich and Soibelman relates it to the Berkovich analytification of X, viewed as a variety over the non-archimedean field of complex Laurent series.
I will explain the ideas of this program and some recent progress in the case of hypersurfaces.