Old and New Physics Prospects for q-Virasoro

 q-deformed Virasoro and W-algebras were defined a quarter century ago with the aim of furthering our understanding of two-dimensional integrable and conformal field theories, while also developing the representation theory of so-called quantum groups. In the last few years, there has been a renewed interest in those algebras, coming rather unexpectedly from the recent success of localization methods in supersymmetric field and string theories. In this talk, I will first review the construction and main features of the deformed algebras; I will then give an overview of some of the more thrilling current developments, such as the existence of non-perturbative Ward identities in supersymmetric gauge theories in various dimensions, along with a dictionary to six-dimensional little string physics.