Zeev Rudnick

Zeev Rudnick (Hebrew זאב רודניק ) is an Israeli mathematician.

Rudnick studied at Bar- Ilan University (Bachelor 1984) at the Hebrew University (Master 's degree in 1985 summa cum laude) and received his PhD in 1990 from Yale University with Ilya Pjatetskij - Shapiro ( and Roger Howe ). 1990 to 1992 he was G. Szegö Assistant Professor at Stanford University, 1992-1996 Assistant Professor at Princeton University and from 1995 first Senior Lecturer, Associate Professor from 1998 and from 2002 professor at the University of Tel Aviv. He was 2003/4 visiting professor at the University of Bristol and is from 2008 to 2010 at the Institute for Advanced Study.

Rudnick deals with the geometry of numbers, with the context of statistics of zeros of zeta functions and the eigenvalues ​​of random matrices (where it partially with Peter Sarnak worked in Princeton ) and beyond with connections between quantum chaos and number-theoretic questions. His investigation with Sarnak of the higher correlations of the zeros distribution of the Riemann zeta function underpinned the context of the eigenvalue distribution of random matrices to classical groups, followed among others in the theory of Katz and Sarnak (for the Sarnak the Cole Prize).

He also dealt with the distribution of zeros of modular forms 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, taking into account the lower bound for the lowest eigenvalue of the Laplace -Beltrami operator on the line defined by a module function Hauptkongruenzfläche significantly towards the suspected by Selberg value quarter improved.

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

Rudnick was Sloan Fellow. In 2001 he received the Erdös Prize. He is a Fellow of the American Mathematical Society.

Writings

  • Editor Andrew Granville: Equidistribution in Number Theory - an introduction, Springer, 2007 ( Proc. NATO Advanced Study Institute, Montreal, 2005 ), in Rudnick, "The arithmetic theory of quantum maps" and Granville " Uniform Distribution", "Torsion points on curves "
  • What is quantum chaos? , Notices of the AMS, Bd.55, No.1, 2008, online as a pdf file
Ilya Piatetski-Shapiro
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