## Quick Facts

Intro | Quantum mathematician |

Is | Mathematician Educator |

From | Israel |

Field | Academia Mathematics |

Gender | male |

## Biography

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. 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 he was a member of the Institute for Advanced Study at Princeton. From 2012, Rudnick is a fellow of the American Mathematical Society.

## 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. Together with Peter Sarnak, he has formulated the Quantum Unique Ergodicity conjectures for eigenfunctions on negatively curved manifolds, 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

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

## Awards and fellowships

- ERC Advanced Grant, 1.7 million euro, 2013–2018.
- Fellow of the American Mathematical Society, 2012–.
- Annales Henri Poincaré Distinguished Paper Award for the year, 2011.
- Erdos prize of the Israel Mathematical Union, 2001.
- Alon Fellow, 1995.
- Sloan Foundation Doctoral Dissertation Fellowship, 1989–1990.

## Selected works

- W. Duke, Z. Rudnick, P. Sarnak, Density of integer points on affine homogeneous varieties, Duke Mathematical Journal 71, 143–179 (1993).
- 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