Greer's research focuses on creating and characterizing classes of materials with multi-scale
microstructural hierarchy, which often combine three-dimensional (3D) architectures with nanoscale-induced material properties. We develop fabrication and syntheses of micro- and nano architected materials using 3D lithography, nanofabrication, and additive manufacturing (AM) techniques, and investigate their mechanical, electrochemical, electromechanical, biochemical, and photonic properties as a function of architecture, constituent materials, and microstructural detail. We strive to uncover the synergy between the internal atomic- and molecular-level microstructure and the multi-scale external dimensionality, where competing material- (nano) and structure- (architecture) induced size effects drive overall response and govern these properties. Specific topics include applications of 3D nano- and micro-architected materials in devices, energy absorbing media, ultra lightweight energy storage systems, filters for chemically-assisted separation, damage-tolerant fabrics, additive manufacturing, and smart, multi-functional materials.