Algebraic Geometry Seminar

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 which emerges in mirror symmetry and in birational geometry, the so-called dual complex of degeneration of varieties. I will show how the techniques of Berkovich geometry give a new insight into the study of dual complexes. In a joint work with Morgan Brown, we determine the homeomorphism type of the dual complex of some degenerations of hyper-Kaehler manifolds. The results are in accordance with the predictions of mirror symmetry, and the recent work about the rational homology of dual complexes of degenerations of hyper-Kaehler varieties, due to Kollar, Laza, Sacca and Voisin. Speaker(s): Enrica Mazzon (Max Planck Institute)