**Proceedings of Symposia in Pure Mathematics**

Volume: 48;
1988;
344 pp;
Softcover

MSC: Primary 00; 01;

Print ISBN: 978-0-8218-1482-6

Product Code: PSPUM/48

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

**Electronic ISBN: 978-0-8218-9343-2
Product Code: PSPUM/48.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

# The Mathematical Heritage of Hermann Weyl

Share this page *Edited by *
*R. O. Wells, Jr.*

Hermann Weyl was one of the most influential mathematicians of
the twentieth century. Viewing mathematics as an organic whole rather
than a collection of separate subjects, Weyl made profound contributions
to a wide range of areas, including analysis, geometry, number theory,
Lie groups, and mathematical physics, as well as the philosophy of
science and of mathematics. The topics he chose to study, the lines of
thought he initiated, and his general perspective on mathematics have
proved remarkably fruitful and have formed the basis for some of the
best of modern mathematical research.

This volume contains the proceedings of the AMS Symposium on
the Mathematical Heritage of Hermann Weyl, held in May 1987 at
Duke University. In addition to honoring Weyl's great accomplishments
in mathematics, the symposium also sought to stimulate the
younger generation of mathematicians by highlighting the cohesive nature
of modern mathematics as seen from Weyl's ideas. The symposium
assembled a brilliant array of speakers and covered a wide range of
topics. All of the papers are expository and will appeal to a broad
audience of mathematicians, theoretical physicists, and other
scientists.

# Table of Contents

## The Mathematical Heritage of Hermann Weyl

- Table of Contents v6 free
- Preface vii8 free
- On induced representations 112 free
- Differentiable structures on fractal-like sets, determined by intrinsic scaling functions on dual Cantor sets 1526
- Representation theory and arithmetic 2536
- Noncommutative algebras and unitary representations 3546
- The oscillator semigroup 6172
- The Classical Groups and invariants of binary forms 133144
- Characters, harmonic analysis, and an L[sup(2)]-Lefschetz formula 167178
- Perspectives on vertex operators and the Monster 181192
- Some problems in the quantization of gauge theories and string theories 199210
- Fully nonlinear elliptic equations 217228
- Surfaces in conformal geometry 227238
- Algebraic cycles, Bott periodicity and the Chern characteristic map 241252
- Uniformization of geometric structures 265276
- Elliptic invariants for differential operators 275286
- New invariants of 3- and 4-dimensional manifolds 285296
- Moduli spaces and homotopy theory 301312
- Fundamental asymmetry in physical laws 317328
- Free fermions on an algebraic curve 329340