Xiaofeng Ren specializes in mathematical analysis of pattern formation, morphology, and morphogenesis problems from physical and biological sciences. He has worked on phase separation theories for block copolymers, Langmuir monolayers, smetic liquid crystals, and systems with long range interaction properties. He develops deep and elegant singular limit theories to study geometric structures such as spikes, vortex lines, phase boundaries. These mathematically rigorous, analytically workable theories reduce complex nonlocal, variational and PDE models to simpler geometric problems. His research has been supported continuously by National Science Foundation and Simons Foundation.