Study on mirror symmetry and noncommutative Hodge structures

同调镜像对称是一种交换辛几何和复代数几何作用的对称。本研究的目的是尝试解决同调镜像对称理论中最重要的问题之一。假设与Calabi-Yau - dg范畴相关的同伦微积分代数的某种形式猜想，我们得到了该范畴泛变形空间上的原始形式和Frobenius结构。

Homological mirror symmetry is a symmetry which interchanges the role of the symplectic geometry and the complex algebraic geometry. The purpose of this research is a trial to solve one of the most important problems in the theory of homological mirror symmetry.Assuming a certain formality conjecture for a homotopy calculas algebra associated to a Calabi-Yau dg category, we obtain a primitive form and hence a Frobenius structure on the versal deformation space for the category.