Abstract:
There are two geometric models for representations of semisimple Lie algebras: one uses affine Grassmannians, the other uses quiver varieties. A long-standing open problem is to relate these two geometric models. I will explain how this has recently been accomplished using symplectic duality. In particular, I will discuss a recent result (joint with Tingley, Webster, Weekes, and Yacobi)
which gives an equivalence of categories between modules for truncated shifted Yangians and modules for Khovanov-Lauda-Rouquier-Webster algebras.