Koszul duality is a powerful mathematical construction. In this talk, I will take a physical perspective to demonstrate one instance of this duality: an algebraic approach to coupling quantum field theories to a quantum mechanical system on a line. I will explain how a Lagrangian coupling results in an algebraic object, called a Maurer-Cartan element, and show that there is a sense in which the Koszul dual to the algebra of local operators gives a “universal coupling”. I will then describe what Koszul duality really “is”, and why many other mathematical constructions deserve the same name.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimedl at PhD students and post-docs but everyone is welcome.