QGM Seminar by Dmitry Sustretov (MPIM Bonn)

Title: Gromov-Hausdorff limits of curves with flat metrics and non-Archimedean geometry

2018.03.05 | Jane Jamshidi

Date Wed 14 Mar
Time 16:15 17:15
Location 1531-215 (Aud.D3)


Two versions of the SYZ conjecture proposed by Kontsevich and Soibelman give a differential-geometric and a non-Archimidean 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, time permitting, will speculate how the techniques used can be extended to higher dimensions.