Keith Promislow’s work blends PDE analysis with dynamical systems techniques to illuminate the interaction of entropy, correlation, and geometry in polymer chemistry, membrane biology, particle systems, and ionic solutions. The goal is to derive reduced dimension descriptions of pattern evolution in energy driven systems and multi-wave interactions in Hamiltonian contexts. He collaborates with plasma physicists, polymer scientists, and computational chemists on derivation of efficient numerical approximations of particle and effective hydrodynamic systems.