Assaf Naor

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Assaf Naor (born May 7, 1975 ) is a Czech-Israeli mathematician .

Life

Naor studied at the Hebrew University in Jerusalem from 1993 , where he obtained his master’s degree in 1998 and his doctorate under Joram Lindenstrauss in 2002 ( Linear and non linear geometric problems in Banach space ). As a post-doc he was at Microsoft Research , where he was a permanent member of the theory group from 2004 to 2007. At the same time he was an Affiliate Assistant Professor at the University of Washington from 2005 to 2008 . Since 2006 he has been Associate Professor of Mathematics at the Courant Institute of Mathematical Sciences of New York University (since 2008 also in the Faculty of Computer Science). He has been a full professor there since 2009.

Naor deals with analysis , probability theory , convex geometry and their applications in computer science , mathematical physics and combinatorics . For example, he and his colleagues succeeded in developing the best known polynomial temporal approximation algorithm for the ( NP-severe ) problem of the most economical cut in networks (Sparsest Cut Problem). In 2008 he received the EMS Prize , with his leading at the time in the laudatory speech Role in non-linear functional analysis was recognized and also fundamental contributions to the combinatorics and theory of algorithms. Naor made important contributions to the Ribe program (after Martin Ribe ).

In 2008 he received the Salem Prize and in 2011 the Bôcher Memorial Prize . He was invited speaker at the ICM 2010 in Hyderabad ( embeddings of the Heisenberg group and fast estimation of graph isoperimetry ). In 2018 he is plenary speaker at the ICM in Rio ( Metric dimension reduction: A snapshot of the Ribe program ) and winner of the Nemmers Prize for Mathematics . He is a fellow of the American Mathematical Society . For 2019 he was awarded the Ostrowski Prize .

In 2004, together with Keith M. Ball , Shiri Artstein and Franck Barthe , he solved Shannon's problem of the monotonous increase in entropy of sums of random variables.

In addition to the Israeli citizenship, he has the Czech citizenship.

Fonts

  • with J. Lee: Extending Lipschitz functions via random metric partitions. Invent. Math. 160 (2005), no. 1, 59-95.
  • with Achlioptas: The two possible values ​​of the chromatic number of a random graph. Ann. of Math. (2) 162 (2005) no. 3, 1335-1351.
  • with Bartal, Linial, Mendel: On metric Ramsey-type phenomena. Ann. of Math. (2) 162 (2005), no. 2, 643-709.
  • with Krauthgamer, J. Lee, Mendel: Measured descent: a new embedding method for finite metrics. Geom. Funct. Anal. 15 (2005), no. 4, 839-858.
  • with Alon, K.Makarychev, Y.Makarychev: Quadratic forms on graphs. Invent. Math. 163 (2006), no. 3, 499-522.
  • with Peres, Schramm and Sheffield: Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces. Duke Math. J. 134 (2006), no. 1, 165-197.
  • with Arora, J. Lee: Euclidean distortion and the sparsest cut. J. Amer. Math. Soc. 21 (2008), no. 1, 1-21
  • with Mendel: Metric cotype. Ann. of Math. (2) 168 (2008), no. 1, 247-298.
  • with Cheeger, Kleiner: Compression bounds for Lipschitz maps from the Heisenberg group to L 1 . Acta Math. 207 (2011), no. 2, 291-373.
  • with J. Fox, Gromov, V. Lafforgue and Pach: Overlap properties of geometric expanders. J. Reine Angew. Math. 671 (2012), 49-83.
  • with Mendel: Ultrametric subsets with large Hausdorff dimension. Invent. Math. 192 (2013), no. 1, 1-54.

literature

Web links

Individual evidence

  1. ↑ It consists in dividing a graph into two parts in such a way that the ratio E / K becomes minimal, with E = number of edges over the section, K = number of nodes in the smaller part of the two halves. The cut should then divide into equal halves if possible and cut a minimum number of edges.
  2. ↑ Naor, James Lee, Sanjeev Arora: Euclidean distortion and the sparsest cut , Proc. 37th ACM Symposium on the Theory of Computing, 2005
  3. ↑ Assaf Naor An introduction to the Ribe Program , Japanese Journal of Mathematics, 7, 2012, 167-233
  4. ^ Ostrowski Prize 2019
  5. ↑ List and biographies of the winners of the ECM 2008, pdf ( Memento of the original from February 1, 2015 in the Internet Archive ) Info: The archive link has been 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.5ecm.nl
personal data
SURNAME Naor, Assaf
BRIEF DESCRIPTION Czech-Israeli mathematician
DATE OF BIRTH May 7th 1975