SYZ Mirror Symmetry and Maurer-Cartan equation

Abstract: The Strominger-Yau-Zaslow conjecture for understanding Mirror Symmetry geometrically, leads to the Fukaya’s conjectural reconstruction of mirror manifolds which solves Maurer-Cartan equation near large limits using quantum corrections. In this talk, we will discuss progesses of the Fukaya’sconjecture and the formulation of the Maurer-Cartan equation near largestructure limits by constructing a dgBV algebra $PV^∗(X)$, a generalized version of the Kodaira–Spencer dgLa, associated to possibly degenerate Calabi–Yau variety equipped with local thickening data. This talk is based onjoint works with Kwokwai Chan, Conan Leung and Yat-Hin Suen.

Mathematics

Audience: researchers in the topic

Emmy Noether Kolloquium Mainz