Peter Sarnak

Peter Sarnak ( born December 18, 1953 in Johannesburg, South Africa) is a South African and American mathematician, the major contributions to number theory and analysis has done.

Life

Sarnak studied until 1974 at the University of Witwatersrand mathematics. He then moved to Stanford University, where he received his doctorate with Paul Cohen in 1980 with a thesis on Prime Geodesic Theorem. From 1980 to 1986 he worked at the Courant Institute of New York University, first as Assistant Professor (until 1983 ), then as an Associate Professor. Subsequently he worked until 1991 as a professor of mathematics at Stanford University. Since 1991 he has been Professor of Mathematics at Princeton University. From 2001 to 2005 he was also Professor at the Courant Institute of New York University. Since 2007, he is one of eight permanent members of the prestigious School of Mathematics of the Institute for Advanced Study in Princeton.

His doctoral include William Duke, Alex Eskin, Jay Jorgenson ( City College of New York), Kannan Soundararajan, Akshay Venkatesh, Jonathan Pila.

Services

Sarnak has published more than 100 scientific works, in which he proved deep results in number theory. The focus will be particularly the relations of the distribution of the zeros of the Riemann zeta function for the so-called Random Matrix Theory ( random matrices to certain classical symmetry groups). With Nicholas Katz, he extended these relationships to other zeta functions of number theory and found analogues for the assumed relationships in the simpler case of function fields. Your together authored book Random Matrices, Frobenius Eigenvalues ​​, and monodromy has the latest developments of analytic number theory significantly influenced (Katz - Sarnak philosophy). Sarnak also found new improved estimates associated with the eigenvalue conjecture of Atle Selberg.

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

Honors

1998 Sarnak was honored with the George Pólya Prize of the Society for Industrial and Applied Mathematics ( SIAM ), 2001 he was awarded the Ostrowski Prize in 2003 and the Levi L. Conant - Prize of the American Mathematical Society. For his work on number theory, he was awarded the 2005 Frank Nelson Cole Prize significant of the American Mathematical Society. In 1990 he was invited speaker at the ICM in Kyoto ( Diophantine problems and linear groups) and in 1998 he gave a plenary lecture at the International Congress of Mathematicians in Berlin (L -functions ).

Since 1991, Sarnak member of the American Academy of Arts and Sciences, since 2002 a member of the National Academy of Sciences. He was inducted into the British Royal Society in 2002. For 2012, the Sarnak Lester Randolph Ford Award was awarded for 2014, the Wolf Prize in Mathematics.

Writings

• With Giuliana Davidoff, Alain Valette: Elementary number theory, group theory and Ramanujan Graphs, Cambridge University Press 2003
• Some Applications of modular forms, Cambridge University Press 1990
• Random matrices, Frobenius eigenvalues ​​and monodromy, American Mathematical Society 1999
• With Quine J. (Editor): Extremal Riemann Surfaces, American Mathematical Society 1997
• With Freydoon Shahidi (Editor): Automorphic forms and applications, American Mathematical Society 2007
• Nicholas M. Katz, Sarnak, " Zeros of zeta functions and symmetries ," Bulletin AMS, Bd.36, 1999, Issue 1, p.1, pdf file, the work won the Conant Price
• Review article by Peter Sarnak for Riemann Hypothesis (PDF file; 150 kB)