Gromov-Hausdorff Limits of Curves with Flat Metrics and Non-Archimedean Geometry

by Prof. Dmitry Sustretov (Max Planck Inst. for Mathematics & IHES)

Friday Feb 23, 2018, 2:30 PM → 3:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Two versions of the SYZ conjecture proposed by Kontsevich and Soibelman give a differential-geometric and a non-Archimedean recipes to find the base of the SYZ fibration associated to a family of Calabi-Yau manifolds with maximal unipotent monodromy. In the first one this space is the Gromov-Hausdorff limit of associated geodesic metric spaces, and in the second one it is a subset of the Berkovich analytification of the associated variety over the field of germs of meromorphic functions over a punctured disc. In this talk I will discuss a toy version of a comparison between the two pictures for maximal unipotent degenerations of complex curves with flat metrics with conical singularities, and speculate how the techniques used can be extended to higher dimensions.