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Nets Hawk Katz is professor of mathematics at the California Institute of Technology. He was a professor of mathematics at Indiana University Bloomington until March 2013.
Katz earned a B.A. in mathematics from Rice University in 1990 at the age of 17. He received his Ph.D. in 1993 under Dennis DeTurck at the University of Pennsylvania, with a dissertation titled "Noncommutative Determinants and Applications".
He is the author of many important results in combinatorics, harmonic analysis and other areas. In 2003, joint with Jean Bourgain and Terence Tao, he proved that any subset of Z/pZ grows substantially under either addition or multiplication. More precisely, if A is a set such that both A.A and A + A have cardinality at most K|A| then A has size at most K^C or at least p/K^C. This result paved the way for subsequent work of Bourgain, Sergei Konyagin and Glibichuk, establishing that every approximate field is almost a field.
Somewhat earlier he was involved in establishing new bounds in connection with the dimension of Kakeya sets. Jointly with Laba and Tao he proved that the Hausdorff dimension of Kakeya sets in 3 dimensions is strictly greater than 5/2, and jointly with Tao he established new bounds in large dimensions.
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