Abstract: The SYZ conjecture is a conjectural geometric explanation of mirror symmetry. Based on this, Kontsevich and Soibelman proposed a non-archimedean approach to mirror symmetry. This led to the notion of essential skeleton and the construction of non-archimedean SYZ fibrations by Nicaise-Xu-Yu.
In this talk, I will introduce these objects and report on recent results extending the approach of Nicaise-Xu-Yu. This yields new types of non-archimedean retractions. For families of quartic K3 surfaces and quintic 3-folds, the new retractions relate nicely with the results on the dual complex of toric degenerations and on the Gromov-Hausdorff limit of the family.
This is based on a work in progress with Léonard Pille-Schneider.
[ L’exposé aura lieu en ligne, sur Zoom. Pour recevoir le lien de connection, contacter l’organisateur LP]