Zeev Rudnick

Rudnick received his PhD from Yale University in 1990 under the supervision of Ilya Piatetski-Shapiro and Roger Evans Howe.{{MathGenealogy|id=39038}}

Rudnick joined Tel Aviv University in 1995, after working as an assistant professor at Princeton and Stanford. In 2003–4 Rudnick was a Leverhulme visiting professor at the University of Bristol and in 2008–2010 and 2015–2016 he was a member of the Institute for Advanced Study at Princeton.

In 2012, Rudnick was inducted as a fellow of the American Mathematical Society.[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society]

Rudnick has been studying different aspects of quantum chaos and number theory. He has contributed to one of the discoveries concerning the Riemann zeta function, namely, that the Riemann zeros appear to display the same statistics as those which are believed to be present in energy levels of quantum chaotic systems and described by random matrix theory.{{cite journal |last=Conrey |first=J. Brian |authorlink=Brian Conrey | title =The Riemann Hypothesis

| journal = Notices of the AMS | volume = 50 | issue = 3 | pages = 352 | year = 2003 | url = http://www.ams.org/notices/200303/fea-conrey-web.pdf}} Together with Peter Sarnak, he has formulated the Quantum Unique Ergodicity conjectures{{cite book |last=Tao |first=Terence |authorlink=Terence Tao |year=2008 |title=Structure and Randomness: Pages from Year One of a Mathematical Blog |url=https://books.google.com/books?id=SzneC0gryvwC&pg=PA236 |publisher=American Mathematical Society |isbn=9780821886281}} for eigenfunctions on negatively curved manifolds,[https://www.sciencedaily.com/releases/2008/10/081010081650.htm Mathematicians Illuminate Deep Connection Between Classical And Quantum Physics, Science Daily] and has investigated the question arising from Quantum Chaos in other arithmetic models such as the Quantum Cat map (with Par Kurlberg) and the flat torus (with CP Hughes and with Jean Bourgain). Another interest is the interface between function field arithmetic and corresponding problems in number fields.

• Ph.D., 1990, Yale University.
• M.Sc., 1985, The Hebrew University, Jerusalem.
• B.Sc., 1984, Bar-Ilan University, Ramat Gan.

• ERC Advanced Grants, 1.7 million euro, 2013–2018.,[http://erc.europa.eu/cordis_search/project_details/106212 Arithmetic and Quantum Chaos, The European Research Council] 2019–2024.
• Fellow of the American Mathematical Society, 2012–.
• Annales Henri Poincaré Distinguished Paper Award for the year, 2011.[https://www.springer.com/birkhauser/physics/journal/23?detailsPage=societies AHP Prizes and Distinguished Papers]
• Erdős Prize of the Israel Mathematical Union, 2001.
• Alon Fellow, 1995.
• Sloan Foundation Doctoral Dissertation Fellowship, 1989–1990.

• {{cite journal|first1=William|last1= Duke|author1-link=William Duke (mathematician)|first2= Zeev|last2= Rudnick|first3= Peter| last3=Sarnak|author3-link=Peter Sarnak| title= Density of integer points on affine homogeneous varieties|journal=Duke Mathematical Journal | volume= 71|pages= 143–179 |year=1993|doi=10.1215/S0012-7094-93-07107-4|mr=1230289|citeseerx=10.1.1.218.5083}}
• Z. Rudnick, P. Sarnak, [https://link.springer.com/article/10.1007%2FBF02099418 The behaviour of eigenstates of arithmetic hyperbolic manifolds], Comm. in Math. Physics 161, 195–213 (1994).
• W. Luo, Z. Rudnick and P. Sarnak, [https://link.springer.com/chapter/10.1007%2F978-3-0348-9102-8_9 On Selberg's eigenvalue conjecture], Geom. and Func. Analysis 5 (1995), 387–401.
• Z. Rudnick and P. Sarnak, [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1077245671 Zeros of principal L-functions and random matrix theory], Duke Mathematical Journal 81 (1996), 269–322 (special volume in honor of J. Nash).
• P. Kurlberg and Z. Rudnick, [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1092749398 Hecke theory and equidistribution for the quantization of linear maps of the torus], Duke Mathematical Journal 103 (2000), 47–78.
• Z. Rudnick and K. Soundararajan, [http://www.pnas.org/content/102/19/6837.full Lower bounds for moments of L-functions], Proc. of the National Academy of Sciences of the USA, 102 (19), (May 10, 2005), 6837–6838.
• Z. Rudnick, [http://www.ams.org/notices/200801/tx080100032p.pdf What is Quantum Chaos?], Notices of the AMS, 55 number 1 (2008), 32–34.
• J. Bourgain and Z. Rudnick, [https://arxiv.org/abs/0907.4824 Restriction of toral eigenfunctions to hypersurfaces], C.R. Math. Acad. Sci. Paris 347 (2009), no 21–22, 1249–1253.
• Jonathan P. Keating and Zeev Rudnick, [http://imrn.oxfordjournals.org/content/early/2012/10/16/imrn.rns220.abstract The variance of the number of prime polynomials in short intervals and in residue classes]. International Mathematics Research Notices 2012; doi: 10.1093/imrn/rns220.
• Alexei Entin, Edva Roditty-Gershon and Zeev Rudnick, [https://arxiv.org/abs/1208.5962 Low-lying zeros of quadratic Dirichlet L-functions, hyper-elliptic curves and Random Matrix Theory], Geom. Funct. Anal. 23 (2013), no. 4, 1230–1261. doi:10.1007/s00039-013-0241-8

{{reflist}}

• [http://www.math.tau.ac.il/~rudnick/ Zeev Rudnick's homepage]
• [https://arxiv.org/find/math/1/au:+Rudnick_Z/0/1/0/all/0/1 Articles by Zeev Rudnick on the Arxiv]
• [http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=242217&vfpref=html&r=1&extend=1 Reviews of publications by Zeev Rudnick by the American Mathematical Society]

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Category:1961 births

Category:Living people

Category:Israeli mathematicians

Category:Academics from Tel Aviv

Category:Fellows of the American Mathematical Society

Category:Yale University alumni

Category:Number theorists

Category:Academic staff of Tel Aviv University

Category:Bar-Ilan University alumni

Category:Hebrew University of Jerusalem alumni

Category:Erdős Prize recipients