Nicholas Katz

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Nicholas Katz in Oberwolfach 2004

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

Life

Nicholas Katz studied at Johns Hopkins University (Bachelor in 1964) and at Princeton University , where he received his master’s degree in 1965 and his doctorate in 1966 with Bernard Dwork with the dissertation On the Differential Equations Satisfied by Period Matrices . He was then an instructor and lecturer , assistant professor in 1968, associate professor in 1971 and professor at Princeton from 1974. From 2002 to 2005 he was chairman of the faculty there. He was visiting scholar at the University of Minnesota , the Universities of Kyoto and Paris ( Paris VI and Orsay) as well as 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 1970/72 Sloan Research Fellow . He has been a member of the American Academy of Arts and Sciences since 2003 and of the National Academy of Sciences since 2004 . In 2003 he and Peter Sarnak received the Levi L. Conant Prize of the American Mathematical Society (AMS) for their essay Zeroes of Zeta Functions and Symmetry in the Bulletin of the American Mathematical Society.

Together with Sarnak, Katz investigated the connection between the eigenvalue distribution of large random matrices of classical groups and the distribution of the distances between the zeros of various and zeta functions in algebraic geometry. He also studied trigonometric sums (such as the Gauss sums important in number theory) using algebro-geometric methods. In 1973 he generalized the concept of the p-adic modular forms introduced shortly before by Jean-Pierre Serre as a p-adic reduction of classic modular forms.

In 2003 he received the Levi L. Conant Prize with Sarnak . In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( p-adic L functions, Serre-Tate local moduli and 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. The second part of SGA 7 (1967 to 1969 at IHES ) was edited by him and Pierre Deligne (they led the seminar, while Grothendieck was increasingly withdrawing from mathematics).

His doctoral students include Mark Kisin and Neal Koblitz as well as William Messing (second reviewer).

Fonts

  • Moments, Monodromy, and Perversity. A Diophantine Perspective. Annals of Mathematical Studies, Princeton 2005, ISBN 0691123306 .
  • Gauss sums, Kloosterman sums, and monodromy groups. Annals of Mathematical Studies, Princeton 1988.
  • 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 0821810170 .
  • With Peter Sarnak: Zeroes of zeta functions and symmetry. Bulletin of the AMS, Vol. 36, 1999, pp. 1-26.

Web links

Individual evidence

  1. ↑ Nicholas Katz in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ Katz, p-adic properties of modular schemes and modular forms, modular functions of one variable, III (Proc. Internat. Summer School, Antwerp 1972), Lecture Notes in Mathematics 350, Springer-Verlag, 1973, pp. 69-190
personal data
SURNAME Katz, Nicholas
ALTERNATIVE NAMES Katz, Nicholas Michael
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH December 7, 1943
PLACE OF BIRTH Baltimore , Maryland