ABSTRACT: “Koszul duality” is a fundamental idea spanning several branches of mathematics, with origins in representation theory and rational homotopy theory. In its simplest incarnation, it relates pairs of algebras (such as symmetric and exterior algebras) that have equivalent categories of representations. Koszul duality also turns out to play a fundamental role in physics, governing the structure of boundary conditions in QFT — in various dimensions, with various amounts of supersymmetry. I will explain the general idea, and give a simple example that leads to a new understanding of gauge/global symmetry in supersymmetric quantum mechanics.