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Nets Hawk Katz (* 1973) ist ein US-amerika … Nets Hawk Katz (* 1973) ist ein US-amerikanischer Mathematiker, der sich insbesondere mit Kombinatorik und Harmonischer Analysis befasst. Katz studierte an der Rice University mit dem Bachelor-Abschluss 1990 mit 17 Jahren und wurde 1993 bei Dennis DeTurck an der University of Pennsylvania promoviert (Noncommutative Determinants and Applications). Als Post-Doktorand war er an der Yale University, der University of Edinburgh und am MSRI. Er war Assistant Professor an der University of Illinois in Chicago und Associate Professor an der Washington University in St. Louis, bevor er Professor an der Indiana University Bloomington wurde. Seit 2013 ist er Professor am Caltech. Er forschte in additiver und geometrischer Kombinatorik, Harmonischer Analysis, geometrischer Maßtheorie und Hydrodynamik. 2010 löste er mit Larry Guth das Problem verschiedener Abstände von Paul Erdős. Er befasst sich auch mit Erweiterungen des Kakeya-Problems, die verbunden sind mit Problemen der Harmonischen Analysis. Dabei arbeitete er unter anderem mit Terence Tao und Izabella Laba zusammen. Mit seinem ehemaligen Studenten fand er die bisher besten Grenzen beim Cap Set Problem. Mit seiner Studentin eröffnete er einen neuen Zugang zur Bildung von Turbulenz (mathematisch Blow Up, Bildung einer Singularität, in endlicher Zeit) bei der Euler- und Navier-Stokes-Gleichung in der Hydrodynamik und entsprechenden Regularitätsfragen der Gleichungen. Das ist eines der Millennium-Probleme. Dabei benutzten sie ein Dyadisches Modell der Gleichungen (dyadische Zerlegung des dreidimensionalen Raumes und Wavelet-Analyse), die auf ein System unendlich vieler, nichtlinear miteinander gekoppelter gewöhnlicher Differentialgleichungen führen. Sie bewiesen in drei Dimensionen bei der Euler-Gleichung und bei der (um einen Diffusionsterm modifizierten) Navier-Stokes-Gleichung mit nicht zu großer Diffusion Blow Up in endlicher Zeit in diesem Modell. 2012 war er Guggenheim Fellow. Er ist Herausgeber des Indiana University Mathematics Journal. 2014 war er Eingeladener Sprecher auf dem ICM in Seoul (The flecnode polynomial: a central object in incidence geometry). 2015 wurde ihm der Clay Research Award zugesprochen. ihm der Clay Research Award zugesprochen.
, Nets Hawk Katz (né en 1973) est un mathématicien américain qui travaille notamment en combinatoire et en analyse harmonique.
, Nets Hawk Katz (1972) é um matemático esta … Nets Hawk Katz (1972) é um matemático estadunidense. É professor de matemática da . Katz obteve o Ph.D. em 1993 orientado por na Universidade da Pensilvânia, com a tese "Noncommutative Determinants and Applications". É autor de diversos resultados fundamentais em combinatória, análise harmônica e outras áreas. Em 2003, juntamente com Jean Bourgain e Terence Tao, provou que qualquer conjunto de Z/pZ cresce substancialmente sob qualquer adição ou multiplicação. Mais precisamente, se A é um conjunto tal que ambos, A.A e A + A tem cardinalidade no mínimo K|A|, então A tem dimensão no mínimo K^C ou pelo menos p/K^C. Este resultado aplainou o caminho para subsequentes trabalhos de Bourgain, Sergei Konyagin e Glibichuk, estabelecendo que todo campo aproximado é geralmente um campo. Pouco anteriormente esteve envolvido em estabelecer novos limites em conexão com a dimensão de . Juntamente com Laba e Tao provou que a dimensão de Hausdorff de conjuntos de Kakeya em 3 dimensões é estritamente maior que 5/2, e juntamente com Tao estabeleceu novos limites e maiores dimensões. Em 2010, Nets Katz publicou com Larry Guth o resultado de um esforço conjunto para resolver o , no qual encontraram um resultado "quase-ótimo", provando que um conjunto de N pontos no plano tem no mínimo cN/log N distâncias distintas.m no mínimo cN/log N distâncias distintas.
, Nets Hawk Katz is the IBM Professor of Mat … Nets Hawk Katz is the IBM 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 several important results in combinatorics (especially additive combinatorics), harmonic analysis and other areas. In 2003, jointly with Jean Bourgain and Terence Tao, he proved that any subset of grows substantially under either addition or multiplication. More precisely, if is a set such that , then has size at most or at least where is a constant that depends on . This result was followed by the 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 Izabella Łaba and Terence Tao he proved that the upper Minkowski dimension of Kakeya sets in 3 dimensions is strictly greater than 5/2, and jointly with Terence Tao he established new bounds in large dimensions. In 2010, Katz along with Larry Guth published the results of their collaborative effort to solve the Erdős distinct distances problem, in which they found a "near-optimal" result, proving that a set of points in the plane has at least distinct distances. In early 2011, in joint work with Michael Bateman, he improved the best known bounds in the cap set problem: if is a subset of of cardinality at least , where , then contains three elements in a line. In 2012, he was named a Guggenheim fellow. During 2011-2012, he was the managing editor of the Indiana University Mathematics Journal. In 2014, he was an invited speaker at the International Congress of Mathematicians at Seoul and gave a talk The flecnode polynomial: a central object in incidence geometry. In 2015, he received the Clay Research Award.2015, he received the Clay Research Award.
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Nets Hawk Katz (* 1973) ist ein US-amerika … Nets Hawk Katz (* 1973) ist ein US-amerikanischer Mathematiker, der sich insbesondere mit Kombinatorik und Harmonischer Analysis befasst. Katz studierte an der Rice University mit dem Bachelor-Abschluss 1990 mit 17 Jahren und wurde 1993 bei Dennis DeTurck an der University of Pennsylvania promoviert (Noncommutative Determinants and Applications). Als Post-Doktorand war er an der Yale University, der University of Edinburgh und am MSRI. Er war Assistant Professor an der University of Illinois in Chicago und Associate Professor an der Washington University in St. Louis, bevor er Professor an der Indiana University Bloomington wurde. Seit 2013 ist er Professor am Caltech.de. Seit 2013 ist er Professor am Caltech.
, Nets Hawk Katz (1972) é um matemático esta … Nets Hawk Katz (1972) é um matemático estadunidense. É professor de matemática da . Katz obteve o Ph.D. em 1993 orientado por na Universidade da Pensilvânia, com a tese "Noncommutative Determinants and Applications". Pouco anteriormente esteve envolvido em estabelecer novos limites em conexão com a dimensão de . Juntamente com Laba e Tao provou que a dimensão de Hausdorff de conjuntos de Kakeya em 3 dimensões é estritamente maior que 5/2, e juntamente com Tao estabeleceu novos limites e maiores dimensões.beleceu novos limites e maiores dimensões.
, Nets Hawk Katz is the IBM Professor of Mat … Nets Hawk Katz is the IBM 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".ommutative Determinants and Applications".
, Nets Hawk Katz (né en 1973) est un mathématicien américain qui travaille notamment en combinatoire et en analyse harmonique.
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Nets Hawk Katz
, Nets Katz
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