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.
https://indico.math.cnrs.fr/event/6807/