Abstract:

Deformations of complex structures on a complex manifold are governed by the famous Kodaira-Spencer DGLA and its Maurer-Cartan equation. On the other hand, tropical geometry deals with piecewise linear objects such as tropical curves and scattering diagrams. These two apparently unrelated subjects are in fact intimately related because they describe respectively the two sides of the mirror symmetry picture. In this talk, I will explain how asymptotic analysis plays the role of the bridge linking these two subjects together; in particular this leads to a proof of a modified version of a conjecture by Fukaya in SYZ mirror symmetry. This talk is based on recent joint works with Naichung Conan Leung and Ziming Nikolas Ma.