My research is in theoretical condensed matter physics, with focus on order, disorder and broken symmetry in many-body systems. Recently we have made significant progress in developing a theory of underdoped high-Tc cuprate superconductors based on a renormalized t-J model which correctly describes the observed phases. In a different area we have discovered a selective ordering mechanism mechanism for the appearance of complex two-dimensional crystalline embedded in an already ordered 3D system.