Mirror symmetry in Schubert calculus

In Schubert calculus we study the cohomology ring of Grassmannians and other geometrically relevant spaces, together with their distinguished bases of Schubert classes. Recent developments include: (a) generalizing the cohomology theory to K theory and further to elliptic cohomology, (b) studying a deformation called h-deformation motivated by Okounkov's theory of stable envelopes, (c) extending the pool of studied spaces from homogeneous spaces to Nakajima quiver varieties and further to Cherkis bow varieties. These three generalizations together reveal a new structure: 3d mirror symmetry in Schubert calculus. The talk is based on joint results with A. Smirnov, A. Varchenko, Z. Zhou, A. Weber, S. Kumar, and a work in progress with Y. Shou.