$R$-matrices from moduli spaces

Abstract: We explain that equivariant (intersection) cohomology groups and hyperbolic restriction give us $R$-matrices satisfying (generalized) Yang-Baxter equations. It is a very general framework, and yields the well-known $R$-matrices of Yangian representations from quiver varieties, as well as those of $W$-algebras from instanton moduli spaces, as examples. Nothing seems to be known in other examples.