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Dr. Kumar primarily conducts research on the boundary of algorithms and the “real world”. His main research interests lie in applying the rich theory of algorithms to the domains of computational geometry, computer graphics, pattern recognition, and machine learning. The general theme that threads his research interests in algorithms is narrowing the gap between theory and practice. Theoretical computer science relies on making assumptions that do not generally hold in the real world. For instance, the performance of algorithms on real data vs worst case analysis, the assumption that all memory operations are unit cost, noise in the input, degeneracies, importance of exact solution to optimization problems are issues that seem to need attention but are mostly ignored by the theory community. Addressing some of these issues has been the focus of his research. His work on core sets illustrates why column generation methods perform well in optimization, both theoretically and experimentally. His work on surface and curve reconstruction gave very simple algorithms that were provably fast and could handle noise in the data. His research on cache oblivious algorithms showed why certain ways to analyze algorithms compared to the RAM model of analysis were better for practical purposes. He also worked on the design of a classifier for biometric and other applications. This classifier has also been used for palm identification using outlines of the human hand. The classifier was based upon ideas that came out from his research in optimization.