Invented algorithms for the manufacture of integrated circuits with features smaller than the wavelength of light used to illuminate the lithographic masks. One conceptual advance was to show that the wavelength of light doesn't actually limit the size of patterns that can be imaged, if we can have multiple exposures.When the desired pattern is smaller than the wavelength, the mask does not look like the pattern, but must instead be discovered by solving an inverse problem. To solve inverse problems efficiently, invented an algorithm for fast incremental convolution, based on the concept of fractal space-filling curves. This algorithm is as fundamental as the famous FFT, which allows fast convolution.

Invented the correct equation for processing vector data with features; for example, removing noise from color images containing edges. This equation is known as "Color TV" and has many applications.

Invented a more realistic notion of fuzzy string matching, and efficient algorithms for finding such matches. Standard fuzzy matching only allows for single-character differences, but both human-generated text and biological genes evolve by large block operations as well.

Designed, developed, and open sourced W3Kit, the world's first graphical web application development toolkit. Applied this toolkit to create the Interactive Gallery of Geometry, an award-winning web site that provided an interactive introduction to a variety of sophisticated mathematical concepts.

Invented theory of residual algebra to study (in collaboration with H. Clemens) the phenomena of deformation theory.