**Proceedings of Symposia in Pure Mathematics**

Volume: 60;
1997;
405 pp;
Hardcover

MSC: Primary 31; 34; 35; 40; 42; 45; 46; 60; 62; 68; 81; 82; 92; 94; 01;

Print ISBN: 978-0-8218-0415-5

Product Code: PSPUM/60

List Price: $102.00

AMS Member Price: $81.60

MAA Member Price: $91.80

**Electronic ISBN: 978-0-8218-9363-0
Product Code: PSPUM/60.E**

List Price: $102.00

AMS Member Price: $81.60

MAA Member Price: $91.80

# The Legacy of Norbert Wiener: A Centennial Symposium

Share this page *Edited by *
*David Jerison; I. M. Singer; Daniel W. Stroock*

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.

#### Readership

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

## The Legacy of Norbert Wiener: A Centennial Symposium

- Contents vii8 free
- Preface ix10 free
- Program xi12 free
- Acknowledgments xix20 free
- Biographical and Historical Remarks 122 free
- Norbert Wiener 324
- The rise and fall of cybernetics in the US and the USSR 2142
- Reminiscences of Norbert Wiener 3152
- Speech by Fagi Levinson 3354
- Some memories of Norbert Wiener 3758
- Pictures 4364
- Scientific Articles 5172
- Gibbs measures, quasi-periodic solutions and nonlnear partial differential equations 5374
- Wiener's Tauberian theorem 6586
- The role of Paley-Wiener theory in partial differential equations 7192
- Paley-Wiener on manifolds 85106
- Norbert Wiener and the development of mathematical engineering 93114
- Oscillating networks of Neurons: Mathematics and function 117138
- Mapping heredity: Using probabilistic models and algorithms to map genes and genomes 137158
- A non-random walk down Wall Street 149170
- Filtered Wiener space versus abstract Wiener space 185206
- Unsolved problems connected with the Wiener criterion 199220
- On the role of the Wiener process in finance theory and practice: The case of replicating portfolios 209230
- Inference, learning, and recognition 223244
- Issues in the mathematical modeling of cortical functioning and thought 235256
- Polymer braids and iterated Moire maps 261282
- Networks that learn and how the brain works 273294
- The risk management revolution 313334
- Complex noncommutative infinite dimensional analysis and Fermion-Boson interactions 329350
- Complex integral transforms, diffraction, resonances and phase space tunneling 355376
- Scaling, the free field and statistical mechanics 373394
- Wiener-Hopf integral equations 391412