Zeev Rudnick

Zeev Rudnick or Ze'ev Rudnick (born 1961 in Haifa, Israel) is a mathematician, specializing in number theory and in mathematical physics, notably quantum chaos. Rudnick is a professor at the School of Mathematical Sciences and the Cissie and Aaron Beare Chair in Number Theory at Tel Aviv University.

Zeev Rudnick
Zeev Rudnick
Born1961 (age 59–60)
Haifa, Israel
Alma materYale University
Hebrew University of Jerusalem
Bar-Ilan University
Awards
Scientific career
FieldsMathematics
InstitutionsTel Aviv University
Doctoral advisorIlya Piatetski-Shapiro
Roger Evans Howe

Education

Rudnick received his Ph.D. from Yale University in 1990 under the supervision of Ilya Piatetski-Shapiro and Roger Evans Howe.[1]

Career

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.[2]

Research

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.[3] Together with Peter Sarnak, he has formulated the Quantum Unique Ergodicity conjectures[4] for eigenfunctions on negatively curved manifolds,[5] 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.

Education

Awards and fellowships


Selected works
  • Duke, William; Rudnick, Zeev; Sarnak, Peter (1993). "Density of integer points on affine homogeneous varieties". Duke Mathematical Journal. 71: 143–179. doi:10.1215/S0012-7094-93-07107-4. MR 1230289.
  • Z. Rudnick, P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Comm. in Math. Physics 161, 195–213 (1994).
  • W. Luo, Z. Rudnick and P. Sarnak, On Selberg's eigenvalue conjecture, Geom. and Func. Analysis 5 (1995), 387–401.
  • Z. Rudnick and P. Sarnak, 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, 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, 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, What is Quantum Chaos?, Notices of the AMS, 55 number 1 (2008), 32–34.
  • J. Bourgain and Z. Rudnick, 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, 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, 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

References
  1. Zeev Rudnick at the Mathematics Genealogy Project
  2. List of Fellows of the American Mathematical Society
  3. Conrey, J. Brian (2003). "The Riemann Hypothesis" (PDF). Notices of the AMS. 50 (3): 352.
  4. Tao, Terence (2008). Structure and Randomness: Pages from Year One of a Mathematical Blog. American Mathematical Society. ISBN 9780821886281.
  5. Mathematicians Illuminate Deep Connection Between Classical And Quantum Physics, Science Daily
  6. Arithmetic and Quantum Chaos, The European Research Council
  7. AHP Prizes and Distinguished Papers
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