Abstract

In this talk, we review the story of constructing miror Calabi-Yau manifold from a Lagrangraintorus fibration, beginning with Fukayas conjectural construction using gradient flow trees and relateit to the Gross-Siebert program via a construction of a Kodaira-Spencer type dgLa. lf time allowswe wil discuss the construction of B-model Frobenius manifold using this dgLa/dgBVa. This is baseon a series of joint work with Kwokwai Chan and Naichung Conan Leung.