Abstract: Stable envelopes are correspondences useful for constructing geometric action of quantum groups and solutions to quantum Knizhnik-Zamolodchikov (qKZ) equations. I will review basic aspects of this and explain the construction in a novel class of examples consisting of certain vortex (also known as quasimap) moduli spaces. The main technical result is that K-theoretic curve counts in these varieties are controlled by qKZ equations with vertex operators of Verma module type (in this talk, I will focus on the sl(2) case).  Applications of the construction include the ramified version of quantum q-Langlands correspondence of Aganagic-Frenkel-Okounkov, and a proposal for categorification of the Gukov-Manolescu invariant of knot complements. This is work in progress with Mina Aganagic.