A quantum group is the mathematical structure responsible for the integrability of quantum systems, it has been formulated by Drinfeld and Jimbo in 1985. More recently, the refined notion of "shifted quantum groups" has played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory. In this talk, I will give a brief introduction to shifted quantum groups, and highlight facts that can be used in the study of integrable systems. Then, I will present an application to algebraic engineering, a newly developed technique to describe the low-energy dynamics of brane systems in string theory.