Research on homotopy algebraic models for geometry

通过构造这样一个例子，我们证明了三角分类的A∞增强一般不是唯一的。另一方面，对于用环面颤振描述的辛流形和复流形之间的同调镜像对称，构造了复流形的非交换变形，将辛流形的变形定义为它们的镜像伙伴，并讨论了这些变形对之间的同调镜像对称成立。

We showed that A∞-enhancements of triangulated categories are not unique in general by constructing such an example.On the other hand, for the homological mirror symmetry between symplectic manifolds and complex manifolds both of which are described by torus fibrations, we constructed noncommutative deformations of the complex manifolds, define deformations of symplectic manifolds as theire mirror partners, and discussed that homological mirror symmectry between these pairs of deformations hold true.