The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations

TL;DR

This survey explores the Strominger-Yau-Zaslow conjecture, its current status, and how it motivates studying mirror symmetry through degenerations of Calabi-Yau manifolds and log structures.

Contribution

It connects the original conjecture to a broader program involving degenerations and log structures in mirror symmetry research.

Findings

Overview of the Strominger-Yau-Zaslow conjecture

Connection between torus fibrations and degenerations

Framework for studying mirror symmetry via degenerations

Abstract

This survey article begins with a discussion of the original form of the Strominger-Yau-Zaslow conjecture, surveys the state of knowledge concering this conjecture, and explains how thinking about this conjecture naturally leads to the program initiated by the author and Bernd Siebert to study mirror symmetry via degenerations of Calabi-Yau manifolds and log structures.