Research on homotopy algebraic models for geometry

通过构造一个这样的例子，证明了三角范畴的∞增强一般不是唯一的；另一方面，对于由环面纤颤描述的辛流形和复流形之间的同调镜像对称性，我们构造了复流形的非对易变形，将辛流形的变形定义为它们的镜象对，并讨论了这些变形对之间的同调镜辛成立。

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.