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Indyk's research focuses primarily on computational geometry in high-dimensions, streaming algorithms, and computational learning theory. He has made a range of contributions to these fields, particularly in the study of low-distortion embeddings, algorithmic coding theory, and geometric and combinatorial pattern matching. He has also made contributions to the theory of compressed sensing. His work on algorithms for computing the Fourier transform of signals with sparse spectra faster than the Fast Fourier transform algorithm was selected by MIT Technology Review as a TR10 Top 10 Emerging Technology in 2012.