Abstract：

Quiver possesses a rich representation theory. On the one hand, it exhibits a deep connection between instantons and coherent sheaves as illuminated by the ADHM construction and the works of many others. On the other hand, quivers also capture the formal deformation space of a Lagrangian submanifold. In this talk, we will discuss these relations more explicitly from the perspective of SYZ mirror symmetry. In particular, we will introduce the notion of framed Lagrangian immersions, the Maurer-Cartan spaces of which are Nakajima quiver varieties. And we will realize the ADHM construction as a mirror symmetry phenomenon. This talk is based on the joint work with Jiawei Hu and Siu-Cheong Lau.