Nick Katz

Nicholas Michael Katz ( born December 7, 1943 in Baltimore, Maryland), also called " Nick Katz ", is an American mathematician who is engaged in algebraic geometry and number theory.

Katz studied at Johns Hopkins University (Bachelor 1964) and at Princeton University, where in 1965 he took his master's degree and doctorate in 1966 with Bernard Dwork with the dissertation On the Differential Equations Satisfied by Period matrices. After that, he was Instructor and Lecturer, Assistant Professor in 1968, Associate Professor in 1971 and from 1974 professor at Princeton. 2002 to 2005 he was Chairman of the Faculty there. He was a visiting scholar at the University of Minnesota, the University of Kyoto and Paris (Paris VI and Orsay ) and at the Institute for Advanced Study and at the Institut des Hautes Études Scientifiques ( IHES ).

In 1968/69 he was a NATO Postdoctoral Fellow, 1975/76 and 1987/88 Guggenheim Fellow and 1971/72 Sloan Fellow. Since 2003 he is member of the American Academy of Arts and Sciences since 2004 and of the National Academy of Sciences. In 2003 he was awarded with Peter Sarnak the Levi L. Conant Prize of the American Mathematical Society ( AMS) for her essay Zeroes of Zeta Functions and Symmetry in the Bulletin of the American Mathematical Society.

Katz examined, inter alia, the compound of Sarnak eigenvalue distribution of large random matrices classical groups and the distribution of the distances between the zero points of different - and Zeta positions in the algebraic geometry. He also studied trigonometric sums ( such as the important in number theory Gauss sums) with algebraic - geometric methods.

His doctoral counts Neal Koblitz. In 2003 he was awarded with the Sarnak Levi L. Conant Prize -. In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki (p- adic L functions, Serre- Tate local moduli and the ratios of solutions of differential equations ) and in 1970 in Nice (The regularity theorem in algebraic geometry ).

Since 2004 he has been editor of the Annals of Mathematics.

His doctoral include Mark Kisin and Neal Koblitz and William Brass ( second supervisor ).

Writings

• Moments, monodromy, and perversity. A Diophantine Perspective. Annals of Mathematical Studies, Princeton 2005, ISBN 0,691,123,306th
• Exponential sums and differential equations. Annals of Mathematical Studies, Princeton 1990.
• Twisted -functions and monodromy. Annals of Mathematical Studies, Princeton 2002.
• Rigid Local Systems. Annals of Mathematical Studies, Princeton 1996.
• With Barry Mazur: Arithmetic moduli of elliptic curves. Princeton 1985.
• With Peter Sarnak: Random Matrices, Frobenius Eigenvalues ​​, and monodromy. AMS Colloquium publications 1998 ISBN 0,821,810,170th
• Zeroes of zeta functions and symmetry: With Peter Sarnak. Bulletin of the AMS, Vol 36, 1999, p.1 - 26th