Scattering diagrams and deformations of holomorphic pairs

Scattering diagrams play a central role in mirror symmetry
as they prescribe how to reconstruct the mirror manifold. Recently,
Chan, Conan Leung and Ma show that studying the asymptotic behaviour of
infinitesimal deformations of the total space of a torus fibration is
governed by scattering diagrams in the sense of Gross Pandharipande and
Siebert. In this talk, I will discuss a generalization of Chan, Leung
and Ma's construction, namely the relation between scattering diagrams
and infinitesimal deformations of pairs $(E, \check{X})$ where $E$ is a
holomorphic vector bundle on a complex manifold $\check{X}$. The new
feature is the extended tropical vertex group where scattering diagrams
are defined.