Mathematical Physics and Algebraic Geometry Seminar

Speaker: Ju Tan (Boston University)

Title: Mirror Construction for Nakajima Quiver Varieties

Abstract: Quiver possesses a rich representation theory. On the one hand, it exhibits a deep connection with 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 Nakajima quiver varieties/ stacks. Besides, we will realize the ADHM construction as a mirror symmetry phenomenon. This is based on the joint work with Jiawei Hu and Siu-Cheong Lau.