Non-archimedean approach to mirror symmetry and to degenerations of varieties

Enrica Mazzon (Bonn)

11-Feb-2021, 11:00-12:00 (3 years ago)

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 a joint work with Morgan Brown and a work in progress with LĂ©onard Pille-Schneider.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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