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Séminaire de Géométrie

École polytechnique  – Salle de conférences du Centre de Mathématiques Laurent Schwartz


11h00 : Enrica Mazzon (Université de Ratisbonne)

"(Non-archimedean) SYZ fibrations for Calabi-Yau hypersurfaces"

Résumé: The SYZ conjecture is a conjectural geometric explanation of mirror symmetry. Based on this, Kontsevich and Soibelman proposed a non-archimedean approach, which led to the construction of non-archimedean SYZ fibrations by Nicaise-Xu-Yu. A recent result by Li relates explicitly the non-archimedean approach to the classical SYZ conjecture.
In this talk, I will focus on maximally degenerate families of Calabi-Yau hypersurfaces in P^n. For a large class of them, in collaboration with Jakob Hultgren, Mattias Jonsson and Nick McCleerey, we solve a non-archimedean conjecture proposed by Li and deduce that classical SYZ fibrations exist on open regions of Calabi-Yau hypersurfaces.


14h00 : Mirko Mauri (ISTA, Vienne)

"Hodge-to-singular correspondence"

Résumé: We show that the cohomology of moduli spaces of Higgs bundles decomposes in elementary
summands depending on the topology of the symplectic singularities on a (fixed!) master object and/or the combinatorics of certain posets and lattice polytopes. This is based on a joint work with Luca Migliorini and Roberto Pagaria.