From deformation theory to tropical geometry

TL;DR

This paper surveys how tropical geometry emerges from the asymptotic analysis of deformation equations on Calabi-Yau manifolds, connecting complex deformation theory with tropical objects.

Contribution

It presents a comprehensive overview of joint work demonstrating the link between deformation theory and tropical geometry through asymptotic analysis.

Findings

Tropical objects arise from asymptotic analysis of Maurer-Cartan equations.

Connections established between complex structure deformations and tropical geometry.

Insights into the geometric transition from complex to tropical structures.

Abstract

This is a write-up of the author's invited talk at the Eighth International Congress of Chinese Mathematicians (ICCM) held at Beijing in June 2019. We give a survey on joint works with Naichung Conan Leung and Ziming Nikolas Ma where we study how tropical objects arise from asymptotic analysis of the Maurer-Cartan equation for deformation of complex structures on a semi-flat Calabi-Yau manifold.