My research involves developing novel geometric algorithms and exploring their applications to various problems in computational biomedicine. In the realm of structural biology, I have been working on deciphering the 3-dimensional shape and architecture of macromolecular assemblies (such as viruses and ribosomes), which hold the very key to the understanding of basic cellular processes, using volumetric density maps produced by cryo-electron microscopy (cryo-EM) and X-ray crystallography. Inherent limitations in these imaging techniques result in insufficient resolutions in the maps (typically much worse than 4 Angstrom), which in turn creates significant computational challenges for automatic structure discovery. The objective of my research is to maximally automate the currently labor-intensive process of structure mining in these density maps by adapting existing, and developing new geometric and image analysis algorithms.