The SYZ conjecture via homological mirror symmetry

TL;DR

This paper introduces the SYZ conjecture within the framework of homological mirror symmetry, providing an accessible exposition aimed at explaining the conjecture's significance and connections in string theory and algebraic geometry.

Contribution

It offers a motivated, introductory perspective on the SYZ conjecture through the lens of homological mirror symmetry, bridging complex geometry and string theory concepts.

Findings

Clarifies the relationship between SYZ conjecture and homological mirror symmetry

Provides an accessible exposition for researchers new to the topic

Connects derived categories with geometric aspects of mirror symmetry

Abstract

These are expository notes based on a talk given at the Superschool on derived categories and D-branes at University of Alberta in July of 2016. The goal of these notes is to give a motivated introduction to the Strominger-Yau-Zaslow (SYZ) conjecture from the point of view of homological mirror symmetry.