Description:

Title: Mirror Construction for Nakajima Quiver Varieties

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 deformation spaces of which are quotient stacks related to Nakajima quiver varieties. Besides, we will realize the ADHM construction as a mirror symmetry phenomenon. If time permits, we will discuss the correspondence between the Maurer-Cartan deformation of Lagrangian immersions and that of special Lagrangian fibers of a SYZ fibration in the affine An case using the formalism of quiver algebroid stacks. This talk is based on the joint work with Jiawei Hu and Siu-Cheong Lau.