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