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K-Theory and Operator Algebras - Proceedings of a Conference Held at the University of Georgia in Athens, Georgia, April 21 -... K-Theory and Operator Algebras - Proceedings of a Conference Held at the University of Georgia in Athens, Georgia, April 21 - 25, 1975 (Paperback, 1977 ed.)
B. B. Morrel, I. M. Singer
R843 Discovery Miles 8 430 Shipped within 7 - 11 working days
Prospects in Mathematics. (AM-70), Volume 70 (Paperback): Friedrich Hirzebruch, Lars Hormander, John Milnor, Jean-Pierre Serre,... Prospects in Mathematics. (AM-70), Volume 70 (Paperback)
Friedrich Hirzebruch, Lars Hormander, John Milnor, Jean-Pierre Serre, I. M. Singer
R1,255 R981 Discovery Miles 9 810 Save R274 (22%) Shipped within 7 - 12 working days

Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.

Vertex Operators in Mathematics and Physics - Proceedings of a Conference November 10-17, 1983 (Paperback, Softcover reprint of... Vertex Operators in Mathematics and Physics - Proceedings of a Conference November 10-17, 1983 (Paperback, Softcover reprint of the original 1st ed. 1985)
James Lepowsky, Stanley Mandelstam, I. M. Singer
R1,914 Discovery Miles 19 140 Out of stock

James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.

Progress in Gauge Field Theory (Paperback, Softcover reprint of the original 1st ed. 1984): Gerard 't Hooft, A. Jaffe, G.... Progress in Gauge Field Theory (Paperback, Softcover reprint of the original 1st ed. 1984)
Gerard 't Hooft, A. Jaffe, G. Lehmann, P.K. Mitter, I. M. Singer
R1,214 Discovery Miles 12 140 Out of stock

The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded con vincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic inter actions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantita tive study of the hadron mass spectrum as well as the role of topo logy in quantum gauge field theory. These problems require for their solution the development and application of non-perturbative methods in quantum gauge field theory. These problems, and their non-pertur bative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory. " In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories. " Lattice gauge theory provides a systematic framework for the investigation of non-perturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the block-spin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed."

The Unity of Mathematics - In Honor of the Ninetieth Birthday of I.M. Gelfand (Hardcover, 2006 ed.): Pavel Etingof, Vladimir S... The Unity of Mathematics - In Honor of the Ninetieth Birthday of I.M. Gelfand (Hardcover, 2006 ed.)
Pavel Etingof, Vladimir S Retakh, I. M. Singer
R3,343 R3,163 Discovery Miles 31 630 Save R180 (5%) Out of stock

(Very preliminary)A tribute to the vision and legacy of Israel Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory. Written by leading mathematicians, the text is broadly divided into two sections: the first is devoted to developments at the intersection of geometry and physics, and the second to representation theory and algebraic geometry. Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program. Graduate students and researchers will benefit from and find inspiration in this broad and unique work, which brings together fundamental results in a number of disciplines and highlights the rewards of an interdisciplinary approach to mathematics and physics.Contributors: M. Atiyah, A. Beilinson, J. Bernstein, A. Connes, P. Deligne, R. Dijkgraaf, D. Gaitsgory, M. Gromov, F. Hirzebruch, M. Hopkins, D. Kazhdan, F. Kirwan, M. Kontsevich, B. Kostant, G. Lusztig, D. McDuff, H. Nakajima, S. Novikov, P. Sarnak, A.

The Chern Symposium 1979 - Proceedings of the International Symposium on Differential Geometry in honor of S.-S. Chern, held in... The Chern Symposium 1979 - Proceedings of the International Symposium on Differential Geometry in honor of S.-S. Chern, held in Berkeley, California, June 1979 (Paperback, Softcover reprint of the original 1st ed. 1980)
M. F. Atiyah; Edited by W.Y. Hsiang; Contributions by Raoul Bott; Edited by S. Kobayashi, I. M. Singer; Contributions by …
R2,430 R2,304 Discovery Miles 23 040 Save R126 (5%) Out of stock

This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S. S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I. M. Singer Contents Real and Complex Geometry in Four Dimensions M. F. ATIYAH. . . . . . . . . . . . . Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS. * . . . * . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH . . . . . * . . . . . . . . . 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER .

Lecture Notes on Elementary Topology and Geometry (Paperback, Softcover reprint of the original 1st ed. 1967): I. M. Singer,... Lecture Notes on Elementary Topology and Geometry (Paperback, Softcover reprint of the original 1st ed. 1967)
I. M. Singer, J.A. Thorpe
R1,010 Discovery Miles 10 100 Out of stock

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis."

Lecture Notes on Elementary Topology and Geometry (Hardcover, Reprint 1976.): I. M. Singer, J.A. Thorpe Lecture Notes on Elementary Topology and Geometry (Hardcover, Reprint 1976.)
I. M. Singer, J.A. Thorpe
R1,056 Discovery Miles 10 560 Out of stock

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis."

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