Stable envelopes, 3d mirror symmetry, bow varieties

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the topic

Algebraic Geometry and Number Theory seminar - ISTA