The Legacy of Norbert Wiener

by Wiener, Norbert; Singer, I. M.; Stroock, Daniel W.; Jerison, David; Singer, I. M.; Stroock, Daniel W.

• ISBN13: 9780821804155
• ISBN10: 0821804154
• Format: Hardcover
• Copyright: 1997-07-01
• Publisher: Amer Mathematical Society

Summary

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. This text will also be of interest to those working in applications.

Table of Contents

Biographical and Historical Remarks: Norbert Weiner

The rise and fall of cybernetics in the US and the USSR

Reminiscences of Norbert Wiener

Speech by Fagi Levinson Some memories of Norbert Wiener

Scientific Articles: Gibbs measures, quasi-periodic solutions and nonlinear partial differential equations

Wiener's Tauberian theorem

The role of Paley-Wiener theory in partial differential equations

Paley-Wiener on manifolds

Norbert Wiener and the development of mathematical engineering

Oscillating networks of neurons: Mathematics and function

Mapping heredity: Using probabilistic models and algorithms to map genes and genomes

A non-random walk down Wall Street

Filtered Wiener space versus abstract Wiener space

Unsolved problems connected with the Wiener criterion

On the role of the Wiener process in finance theory and practice: The case of replicating portfolios

Inference, learning, and recognition

Issues in the mathematical modeling of cortical functioning and thought

Polymer braids and iterated Moire maps

Networks that learn and how the brain works

The risk management revolution

Complex noncommutative infinite dimensional analysis and Fermion-Boson interactions

Complex integral transforms, diffraction, resonances and phase space tunneling

Scaling, the free field and statistical mechanics

Weiner-Hopf integral equations

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