Zeev Rudnick

Zeev Rudnick ( Hebrew זאב רודניק; born in Haifa in 1961 ) is an Israeli mathematician.

Rudnick studied at the Bar Ilan University (Bachelor 1984), at the Hebrew University (Master’s degree 1985 summa cum laude) and received his doctorate in 1990 from Yale University under Ilya Pjatetskij-Shapiro (and Roger Howe ). From 1990 to 1992 he was G. Szegö Assistant Professor at Stanford University , from 1992 to 1996 Assistant Professor at Princeton University and from 1995 initially Senior Lecturer, from 1998 Associate Professor and from 2002 Professor at Tel Aviv University . He was visiting professor at Bristol University in 2003/04 and at the Institute for Advanced Study from 2008 to 2010 .

Rudnick deals with the geometry of numbers, with the connection between the statistics of the zeros of zeta functions and the eigenvalues of random matrices (where he partly worked with Peter Sarnak at Princeton) and also with connections between quantum chaos and questions of number theory. His investigation with Sarnak of the higher correlations of the zero point distribution of the Riemann zeta function underpinned the connection with the eigenvalue distribution of random matrices to classical groups, further pursued in the theory of Katz and Sarnak (for which Sarnak received the Cole Prize ).

He also dealt with the distribution of the zeros of modular shapes and the zeros of zeta functions of hyperelliptic curves. With W. Luo and Sarnak he also worked on the eigenvalue conjecture of Atle Selberg in spectral geometry, whereby the lower limit for the lowest eigenvalue of the Laplace-Beltrami operator on the main congruence surface defined by a module function is considerably in the direction of the value assumed by Selberg 1/4 improved.

The Quantum Unique Ergodicity Conjecture (QUE, 1991) comes from him and Sarnak , partially solved by Elon Lindenstrauss , Kannan Soundararajan and Roman Holowinsky .

Rudnick was a Sloan Fellow. In 2001 he received the Erdős Prize . He is a fellow of the American Mathematical Society . In 2014 he was invited speaker at the ICM in Seoul ( Some problems in analytic number theory for polynomials over a finite field ).

Fonts

Editor with Andrew Granville : Equidistribution in Number Theory - an introduction. Springer 2007 (Proc. NATO Advanced Study Institute, Montreal 2005), in it by Rudnick “The arithmetic theory of quantum maps” and with Granville “Uniform Distribution”, “Torsion points on curves”.
What is quantum chaos? Notices of the AMS, Vol. 55, No. 1, 2008, online as PDF.

Web links

Homepage
Literature by and about Zeev Rudnick in the bibliographic database WorldCat

Individual evidence

^ Zeev Rudnick, Peter Sarnak: The n-level correlations of zeros of the Zetafunction. In: Comptes Rendus de l'Acadèmie des Sciences / 2. Vol. 319 (1994), p. 1027, ISSN 0249-6305 .
^ Wenzhi Luo, Zeev Rudnick, Peter Sarnak: On Selbergs Eigenvalue conjecture. In: Geometric and Functional Analysis. 5: 387 (1995), ISSN 1016-443X ; see Peter Sarnak: On Selbergs Eigenvalue Conjecture. (PDF; 217 kB). In: Notices of the American Mathematical Society. 1995, ISSN 0002-9920 .

personal data
SURNAME	Rudnick, Zeev
ALTERNATIVE NAMES	זאב רודניק (Hebrew)
BRIEF DESCRIPTION	Israeli mathematician
DATE OF BIRTH	1961
PLACE OF BIRTH	Haifa

[1] Zeev Rudnick, Peter Sarnak: The n-level correlations of zeros of the Zetafunction. In: Comptes Rendus de l'Acadèmie des Sciences / 2. Vol. 319 (1994), p. 1027, ISSN 0249-6305 .

[2] Wenzhi Luo, Zeev Rudnick, Peter Sarnak: On Selbergs Eigenvalue conjecture. In: Geometric and Functional Analysis. 5: 387 (1995), ISSN 1016-443X ; see Peter Sarnak: On Selbergs Eigenvalue Conjecture. (PDF; 217 kB). In: Notices of the American Mathematical Society. 1995, ISSN 0002-9920 .