3D shape matching, massive dataset visualization, and protein structure prediction. The theoretical issues involve combinatorial geometry, algorithm design and basic complexity theory. This effort is aimed at deriving new computational methods for solving problems of a geometric or biological nature that have resisted past investigations because of one two reasons: either the input data is too massive to be processed directly and it can only be "sampled" cleverly or the number of variables is itself so high that standard methods suffer from an exponential blowup in the time it takes to run them. New dimension reduction techniques are needed to resolve this bottleneck.
