Nets cat

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Nets Hawk Katz (* 1973 ) is an American mathematician who specializes in combinatorics and harmonic analysis .

Katz graduated from Rice University with a bachelor's degree in 1990 at the age of 17 and received his doctorate in 1993 under Dennis DeTurck at the University of Pennsylvania (Noncommutative Determinants and Applications). He was a post-doctoral student at Yale University , the University of Edinburgh and MSRI . He was an assistant professor at the University of Illinois at Chicago and an associate professor at Washington University in St. Louis before becoming a professor at Indiana University Bloomington . He has been a professor at Caltech since 2013 .

He conducted research in additive and geometric combinatorics, harmonic analysis, geometric dimension theory and hydrodynamics. In 2010 he and Larry Guth solved the problem of different distances from Paul Erdős . He also deals with extensions of the Kakeya problem that are related to problems in harmonic analysis. He worked with Terence Tao and Izabella Laba , among others .

With his former student Michael Bateman , he found the best limits so far in the cap set problem .

With his student Natasa Pavlovic he opened up a new approach to the formation of turbulence (mathematically blow-up , formation of a singularity, in finite time) in the Euler and Navier-Stokes equation in hydrodynamics and corresponding regularity questions of the equations. That is one of the Millennium Problems . They used a Dyadic model of equations (dyadic decomposition of the three-dimensional space and wavelet analysis), the infinitely lead to a system of many non-linear ordinary differential equations coupled with each other. They proved in three dimensions with the Euler equation and with the Navier-Stokes equation (modified by a diffusion term) with not too large a diffusion blow up in finite time in this model.

In 2012 he was a Guggenheim Fellow . He is the editor of the Indiana University Mathematics Journal. In 2014 he was invited speaker at the ICM in Seoul (The flecnode polynomial: a central object in incidence geometry). In 2015 he was awarded the Clay Research Award .

Web links

Individual evidence

  1. ↑ Biography at Indiana University on the occasion of the Guggenheim Fellowship ( Memento of the original from September 27, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.iu.edu
  2. ↑ Nets Katz in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. ^ Faculty list Caltech 2013
  4. ↑ Guth, Katz, On the Erdös distinct distances problem in the plane , Annals of Mathematics, Volume 181, 2015, pp. 155–190, Arxiv 2010
  5. ^ Katz, Tao New bounds for Kakeya problems , J. Anal. Math. 87, 2002, 231-263
  6. ↑ Katz, Laba, Tao An improved bound on the Minkowski dimension of Besicovitch sets in R3 , Annals of Mathematics, 152, 2000, 383–446
  7. ^ Bateman, Katz New bounds on Cap Sets , Journal of the American Mathematical Society, 25, 2012, 585–613
  8. ^ Katz, Pavlovic Finite time blow up for a dyadic model of the Euler equations , Transactions AMS, 357, 2005, 695-708, online
  9. ↑ Katz, Pavlovic A cheap Caffarelli — Kohn — Nirenberg inequality for the Navier — Stokes equation with hyper-dissipation , Geometric and Functional Analysis, 12, 2002, 355-379
  10. ↑ 2015 Clay Research Award
personal data
SURNAME Katz, Nets
ALTERNATIVE NAMES Katz, Nets Hawk (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH 1973