TiTle:  Localized mirror functor and Nakajima quiver varieties

Abstract:  In this talk, I will first review the construction of localized mirror functor in my joint work with Cheol-Hyun Cho and Hansol Hong. We start by using the example of an immersed sphere, which is the main ingredient in the mirror construction of Gr(2,n) in joint work with Hansol Hong and Yoosik Kim. Then we revisit the quiver mirror construction and introduce ranks and framing. We showed that framed immersed Lagrangian surfaces produce a localized mirror functor to Nakajima quiver varieties in a joint work with Jiawei Hu and Ju Tan.