Nets Katz

Nets Hawk Katz (born 1973 ) is an American mathematician who is particularly concerned with Combinatorics and Harmonic Analysis.

Katz studied at Rice University with a bachelor's degree in 1990 at age 17, and was founded in 1993 with Dennis Deturck at the University of Pennsylvania PhD ( Noncommutative Determinants and Applications ). As a post - graduate student he was at Yale University, the University of Edinburgh and at MSRI. He was Assistant Professor at the University of Illinois at Chicago and an associate professor at Washington University in St. Louis, before he became a professor at Indiana University in Bloomington. Since 2013 he is a professor at Caltech.

He conducted research in additive and geometric combinatorics, harmonic analysis, geometric measure theory and hydrodynamics. In 2010 he broke with Larry Guth, the problem of different distances of Paul Erdős. It also deals with extensions of the Kakeya problem associated with problems of harmonic analysis. He has worked with, among others, Terence Tao and Izabella Laba.

With his former student Michael Bateman he found the previous best limits in Cap Set problem.

With its student Natasa Pavlovic, he opened a new approach to the formation of turbulence ( mathematically Blow Up, formation of a singularity in finite time ) for the Euler and Navier -Stokes equation in hydrodynamics and corresponding Regularitätsfragen the equations. This is one of the Millennium problems. They used a dyadic model of equations ( dyadic decomposition of the three-dimensional space and wavelet analysis ) that lead to a system of infinitely many non-linear ordinary differential equations coupled with each other. They showed in three dimensions in the Euler equation and the (modified a diffusion term ) Navier-Stokes equation is not too large diffusion blow up in finite time in this model.

In 2012 he was Guggenheim Fellow. He is the editor of the Indiana University Mathematics Journal.