Modul: MAT075 Zurich Graduate Colloquium

## What is... homological mirror symmetry?

Vortrag von Patricia Dietzsch

**Datum:** 18.05.21 **Zeit:** 16.15 - 18.30 **Raum:** Online

The phenomenon of mirror symmetry was first observed in the 1980's by physicists who realised that distinct manifolds can be used to construct equivalent models in string theory. The mathematical framework to explain these observations has been formulated by Kontsevich in 1994. His Homological Mirror Symmetry (HMS) conjecture predicts a close connection between the symplectic geometry of a Calabi-Yau manifold and the algebraic geometry of "its mirror-dual" complex algebraic manifold. In this talk, I'd like to share an informal view on the subject, trying to explain what the conjecture is about, without assuming any knowledge in symplectic or algebraic geometry. We will then focus on the specific case of elliptic curves, for which the HMS conjecture has been proved by Polishchuk and Zaslow in 1998. We follow closely Andrew Port's introductory paper from 2015.