Zeev Rudnick or Ze'ev Rudnick (born 1961 in

Haifa Haifa ( he, חֵיפָה ' ; ar, حَيْفَا ') is the third-largest city in Israel—after Jerusalem and Tel Aviv—with a population of in . The city of Haifa forms part of the Haifa metropolitan area, the third-most populous metropol ...

, Israel) is a mathematician, specializing in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and in

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

, notably

quantum chaos Quantum chaos is a branch of physics which studies how chaos theory, chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship betwee ...

. Rudnick is a professor at the School of Mathematical Sciences and the Cissie and Aaron Beare Chair in Number Theory at

Tel Aviv University Tel Aviv University (TAU) ( he, אוּנִיבֶרְסִיטַת תֵּל אָבִיב, ''Universitat Tel Aviv'') is a public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Locate ...

Education

Rudnick received his PhD from

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

in 1990 under the supervision of

Ilya Piatetski-Shapiro Ilya Piatetski-Shapiro (Hebrew: איליה פיאטצקי-שפירו; russian: Илья́ Ио́сифович Пяте́цкий-Шапи́ро; 30 March 1929 – 21 February 2009) was a Soviet-born Israeli mathematician. During a career that sp ...

and

Roger Evans Howe Roger Evans Howe (born May 23, 1945) is the William R. Kenan, Jr. Professor Emeritus of Mathematics at Yale University, and Curtis D. Robert Endowed Chair in Mathematics Education at Texas A&M University. He is known for his contributions to rep ...

Career

Rudnick joined Tel Aviv University in 1995, after working as an assistant professor at

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine ...

and

Stanford Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considere ...

. In 2003–4 Rudnick was a

Leverhulme The Leverhulme Trust () is a large national grant-making organisation in the United Kingdom. It was established in 1925 under the will of the 1st Viscount Leverhulme (1851–1925), with the instruction that its resources should be used to suppo ...

visiting professor at the

University of Bristol , mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type ...

and in 2008–2010 and 2015–2016 he was a member of the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

at Princeton. In 2012, Rudnick was inducted as a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

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 The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...

, 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 In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

. Together with

Peter Sarnak Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced St ...

, 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 Jean, Baron Bourgain (; – ) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic t ...

). Another interest is the interface between function field arithmetic and corresponding problems in number fields.

Education

*Ph.D., 1990,

. *M.Sc., 1985,

The Hebrew University The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

, Jerusalem. *B.Sc., 1984,

Bar-Ilan University Bar-Ilan University (BIU, he, אוניברסיטת בר-אילן, ''Universitat Bar-Ilan'') is a public research university in the Tel Aviv District city of Ramat Gan, Israel. Established in 1955, Bar Ilan is Israel's second-largest academic i ...

, Ramat Gan.

Awards and fellowships

* ERC Advanced Grants, 1.7 million euro, 2013–2018.Arithmetic and Quantum Chaos, The European Research Council
/ref>, 2019–2024. *Fellow of the

, 2012–. *

Annales Henri Poincaré The ''Annales Henri Poincaré'' (''A Journal of Theoretical and Mathematical Physics'') is a peer-reviewed scientific journal which collects and publishes original research papers in the field of theoretical and mathematical physics. The emphasis ...

Distinguished Paper Award for the year, 2011.AHP Prizes and Distinguished Papers
/ref> *

Erdős Prize The Anna and Lajos Erdős Prize in Mathematics is a prize given by the Israel Mathematical Union to an Israeli mathematician (in any field of mathematics and computer science), "with preference to candidates up to the age of 40." The prize was e ...

of the

Israel Mathematical Union The Israel Mathematical Union (IMU) ( he, הַאִיגּוּד הַיִשְׂרְאֵלִי לְמָתֶמָטִיקָה) is an association of professional mathematicians in Israel. It is a member of the European Mathematical Society and the Inte ...

, 2001. *Alon Fellow, 1995. *

Sloan Foundation The Alfred P. Sloan Foundation is an American philanthropic nonprofit organization. It was established in 1934 by Alfred P. Sloan Jr., then-president and chief executive officer of General Motors. The Sloan Foundation makes grants to support or ...

Doctoral Dissertation Fellowship, 1989–1990.

Selected works

* *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

External links

Zeev Rudnick's homepage

Articles by Zeev Rudnick on the Arxiv
{{DEFAULTSORT:Rudnick, Zeev 1961 births Living people Israeli mathematicians People from Tel Aviv Fellows of the American Mathematical Society Yale University alumni Number theorists Tel Aviv University faculty Bar-Ilan University alumni Hebrew University of Jerusalem alumni Erdős Prize recipients