From deformation theory to tropical geometry

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 the papers [6,7] where the author and his collaborators Naichung Conan Leung and Ziming Nikolas Ma 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. Contents 1. Background 1 2. The link -SYZ mirror symmetry 3 3. Scattering diagrams from Maurer-Cartan elements 6 4. Tropical counting from Maurer-Cartan elements 11 5. Epilogue 15 Acknowledgment 16 References 16