Speaker: Enrica Mazzon (MPI Bonn)
Title: Non-archimedean approach to mirror symmetry and to degenerations of varieties
Speaker's URL: https://sites.google.com/view/enrica-mazzon/home-page
Abstract: Mirror symmetry is a fast-moving research area at the boundary between mathematics and theoretical physics. Originated from observations in string theory, it suggests that complex Calabi-Yau manifolds should come in mirror pairs, in the sense that geometrical information of a Calabi-Yau manifold can be read through invariants of its mirror.
In the first part of the talk, I will introduce some geometrical ideas inspired by mirror symmetry. In particular, I will go through the main steps which relate mirror symmetry to non-archimedean geometry and the theory of Berkovich spaces.
In the second part, I will describe a combinatorial object, the so-called dual complex of a degeneration of varieties. This emerges in many contexts of algebraic geometry, including mirror symmetry where moreover it comes equipped with an integral affine structure. I will show how the techniques of Berkovich geometry give a new insight into the study of dual complexes and their integral affine structure. This is based on joint work with Morgan Brown and a work in progress with Léonard Pille-Schneider.
URL associated with Seminar
https://research.math.osu.edu/agseminar/