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The Mathematical Heritage of Hermann Weyl
Edited by: R. O. Wells, Jr., Rice University, Houston, TX
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Proceedings of Symposia in Pure Mathematics
1988; 344 pp; softcover
Volume: 48
Reprint/Revision History:
fourth printing 2000
ISBN-10: 0-8218-1482-6
ISBN-13: 978-0-8218-1482-6
List Price: US$47
Member Price: US$37.60
Order Code: PSPUM/48
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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

  • R. Bott -- On induced representations
  • D. Sullivan -- Differentiable structures on fractal-like sets, determined by intrinsic scaling functions on dual Cantor sets
  • R. P. Langlands -- Representation theory and arithmetic
  • D. A. Vogan, Jr. -- Noncommutative algebras and unitary representations
  • R. Howe -- The oscillator semigroup
  • R. Howe -- The Classical Groups and invariants of binary forms
  • J. Arthur -- Characters, harmonic analysis, and an \(L^2\)-Lefschetz formula
  • J. Lepowsky -- Perspectives on vertex operators and the Monster
  • I. M. Singer -- Some problems in the quantization of gauge theories and string theories
  • L. Nirenberg -- Fully nonlinear elliptic equations
  • R. L. Bryant -- Surfaces in conformal geometry
  • H. B. Lawson, Jr. and M.-L. Michelsohn -- Algebraic cycles, Bott periodicity and the Chern characteristic map
  • S.-T. Yau -- Uniformization of geometric structures
  • R. G. Douglas -- Elliptic invariants for differential operators
  • M. Atiyah -- New invariants of 3- and 4-dimensional manifolds
  • C. H. Taubes -- Moduli spaces and homotopy theory
  • R. Penrose -- Fundamental asymmetry in physical laws
  • E. Witten -- Free fermions on an algebraic curve
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