We survey a recent development which connects quantum integrable models with Schubert calculus for quiver varieties: there is a purely geometric construction of solutions to the Yang-Baxter equation and their associated Yang-Baxter algebras which play a central role in quantum integrable systems and exactly solvable lattice models in statistical physics. We will provide a simple but explicit example using the classical geometry of Grassmannians in order to explain some of the main ideas. We consider the degenerate five-vertex limit of the asymmetric six-vertex model and identify its associated Yang-Baxter algebra as convolution algebra arising from the equivariant Schubert calculus of Grassmannians. We show how our method can be used to construct (Schur algebra type) quotients of the universal enveloping algebra of the current algebra gl2 [t] acting on the tensor product of copies of its evaluation representation C2 [t]. Finally we connect it with the COHA for the A1-quiver.