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The Legacy of Norbert Wiener: A Centennial Symposium
Edited by: David Jerison, I. M. Singer, and Daniel W. Stroock, Massachusetts Institute of Technology, Cambridge, MA

Proceedings of Symposia in Pure Mathematics
1997; 405 pp; hardcover
Volume: 60
ISBN-10: 0-8218-0415-4
ISBN-13: 978-0-8218-0415-5
List Price: US$102
Member Price: US$81.60
Order Code: PSPUM/60
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This book contains lectures presented at the MIT symposium on the 100th anniversary of Norbert Wiener's birth held in October 1994. The topics reflect Wiener's main interests while emphasizing current developments.

In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener-Hopf theory, and Paley-Wiener theory, the book discusses the following topics:

  • Fourier integral operators with complex phase (a contemporary successor to the Paley-Wiener theory)
  • statistical aspects of quantum mechanics and of liquid crystals
  • financial markets, including the new trading strategies for options based on Wiener processes
  • statistical methods of genetic research
  • models of the nervous system, pattern recognition, and the nature of intelligence

The volume includes reviews on Norbert Wiener's contributions from historical and current perspectives.

This book gives mathematical researchers an overview of new mathematical problems presented by other areas and gives researchers in other fields a broad overview of the ways in which advanced mathematics might be useful to them.


Graduate students, mathematicians, statisticians, science historians, researchers and professionals in fields that use mathematics, such as molecular- and neurobiology, brain and cognitive science, electrical engineering, computer science, economics, technical financial analysis, and physics.

Table of Contents

Biographical and Historical Remarks
  • D. Jerison and D. W. Stroock -- Norbert Weiner
  • P. Elias -- The rise and fall of cybernetics in the US and the USSR
  • D. Struik -- Reminiscences of Norbert Wiener
  • Speech by Fagi Levinson
  • P. A. Samuelson -- Some memories of Norbert Wiener
Scientific Articles
  • J. Bourgain -- Gibbs measures, quasi-periodic solutions and nonlinear partial differential equations
  • L. Carleson -- Wiener's Tauberian theorem
  • L. Ehrenpreis -- The role of Paley-Wiener theory in partial differential equations
  • V. Guillemin -- Paley-Wiener on manifolds
  • T. Kailath -- Norbert Wiener and the development of mathematical engineering
  • N. Kopell -- Oscillating networks of neurons: Mathematics and function
  • E. S. Lander -- Mapping heredity: Using probabilistic models and algorithms to map genes and genomes
  • A. W. Lo -- A non-random walk down Wall Street
  • P. Malliavin -- Filtered Wiener space versus abstract Wiener space
  • V. Maz'ya -- Unsolved problems connected with the Wiener criterion
  • R. C. Merton -- On the role of the Wiener process in finance theory and practice: The case of replicating portfolios
  • S. K. Mitter -- Inference, learning, and recognition
  • D. Mumford -- Issues in the mathematical modeling of cortical functioning and thought
  • D. R. Nelson and R. D. Kamien -- Polymer braids and iterated Moiré maps
  • T. Poggio -- Networks that learn and how the brain works
  • C. S. Sanford, Jr. and D. Borge -- The risk management revolution
  • I. Segal -- Complex noncommutative infinite dimensional analysis and Fermion-Boson interactions
  • J. Sjöstrand -- Complex integral transforms, diffraction, resonances and phase space tunneling
  • T. Spencer -- Scaling, the free field and statistical mechanics
  • H. Widom -- Weiner-Hopf integral equations
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