Peter Sarnak

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


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

His PhD students include William Duke , Alex Eskin , Jay Jorgenson (City College of New York), Kannan Soundararajan , Akshay Venkatesh , Jonathan Pila, and Jacob Tsimerman .


Sarnak has published more than 100 scientific papers in which he demonstrated profound results in number theory. The focus is on the relationship between the distribution of the zeros of the Riemann zeta function and the so-called Random Matrix Theory (random matrices for certain classical symmetry groups). With Nicholas Katz , he expanded these relationships to further zeta functions of number theory and found analogues for the assumed relationships in the simpler case of function fields. Their book Random Matrices, Frobenius Eigenvalues, and Monodromy , which they wrote together, has significantly influenced the current developments in analytical number theory ( Katz-Sarnak philosophy ). Sarnak also found new improved estimates related to Atle Selberg's eigenvalue conjecture .

The Quantum Unique Ergodicity Conjecture (QUE, 1991) comes from him and Zeev Rudnick , partially solved by Elon Lindenstrauss , Kannan Soundararajan and Roman Holowinsky . One of Sarnak's conjectures concerns the random behavior of the Möbius function .

In 1988 he introduced Ramanujan graphs with Alexander Lubotzky and Ralph Phillips .


In 1998 Sarnak was honored with the George Pólya Prize of the Society for Industrial and Applied Mathematics (SIAM), in 2001 he received the Ostrowski Prize and in 2003 the Levi L. Conant Prize of the American Mathematical Society . In 2005 he was awarded the Frank Nelson Cole Prize of the American Mathematical Society for his work on number theory . 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 ).

From 1983 to 1985, Sarnak was a Sloan Research Fellow . He has been a member of the American Academy of Arts and Sciences since 1991 and of the National Academy of Sciences since 2002 . In 2002 he was accepted into the British Royal Society . For 2012 Sarnak was awarded the Lester Randolph Ford Award , for 2014 the Wolf Prize in Mathematics and for 2019 the New Year's Eve Medal of the Royal Society. He has been an external member of the Academia Europaea since 2013 . He is a member of the American Philosophical Society and a Fellow of the American Mathematical Society .


See also

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. Luo, Zeev Rudnick , Sarnak “On Selbergs Eigenvalue Conjecture”, Geom.Funct.Analysis, Vol. 5, 1995, p. 387, see Sarnak “On Selbergs Eigenvalue Conjecture”, Notices AMS, 1995, PDF file
  3. Alexander Lubotzky, Ralph Phillips, Peter Sarnak: Ramanujan graphs. Combinatorica, Vol. 8, 1988, pp. 261-277
  4. ↑ Directory of members: Peter Sarnak. Academia Europaea, accessed January 20, 2018 (English, with biographical and other information).