Stable envelopes, 3d mirror symmetry, bow varieties

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

The role played by Schubert classes in the geometry of Grassmannians is played by the so-called stable envelopes in the geometry of Nakajima quiver varieties. Stable envelopes come in three flavors: cohomological, K theoretic, and elliptic stable envelopes. We will show examples, and explore their appearances in enumerative geometry and representation theory. In the second part of the talk we will discuss 3d mirror symmetry for characteristic classes’’, namely, the fact that for certain pairs of seemingly unrelated spaces the elliptic stable envelopes match’ in some concrete (but non-obvious) sense. We will meet Cherkis bow varieties, a pool of spaces (conjecturally) closed under 3d mirror symmetry for characteristic classes’’. The combinatorics necessary to play Schubert calculus on bow varieties includes binary contingency tables, tie diagrams, and the Hanany-Witten transition.