I will describe an algebraic variety associated to an algebra of finite representation type. Starting from an orientation of a type A_n quiver, one gets a curvy version of the associahedron, while in general one gets a variety whose totally positive part encodes the tau-tilting theory of the algebra. Many mysteries about this construction remain, including how to define a similar variety when the algebra is not of finite representation type. This is part of joint work with Nima Arkani-Hamed, Hadleigh Frost, Pierre-Guy Plamondon, and Giulio Salvatori. Part of the motivation comes from string theory, which I will attempt to explain if I have time.