Von Neumann's Method of Alternating Projections seeks a common point in two subsets of a Euclidean space. This simple heuristic has long proved popular in diverse computational applications, even for sets that may be nonsmooth, like polyhedra, or nonconvex, like manifolds of low-rank matrices. I will sketch how the classical idea of transversality extends to arbitrary closed sets, and how it controls the rate of convergence of alternating projections.

Joint work with D. Drusvyatskiy and A. Ioffe