Victor W Guillemin's Books

Mathematics Past and Present Fourier Integral Operators

By: J.J. Duistermaat,Victor W Guillemin,Jochen Brüning,L. Hörmander

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Mathematics Past and Present Fourier Integral Operators

By: J.J. Duistermaat,Victor W Guillemin,Jochen Brüning,L. Hörmander

What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hörmander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well.

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Page Count

300

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540567410

ISBN 13

9783540567417

Supersymmetry and Equivariant de Rham Theory

By: Victor W Guillemin,Shlomo Sternberg

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Supersymmetry and Equivariant de Rham Theory

By: Victor W Guillemin,Shlomo Sternberg

This book discusses the equivariant cohomology theory of differentiable manifolds. Although this subject has gained great popularity since the early 1980's, it has not before been the subject of a monograph. It covers almost all important aspects of the subject The authors are key authorities in this field.

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Page Count

243

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Springer Science & Business Media

Published Date

ISBN 10

3662039923

ISBN 13

9783662039922

Toric Topology

By: Victor M. Buchstaber,Taras E. Pano

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Toric Topology

By: Victor M. Buchstaber,Taras E. Pano

This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.

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Page Count

534

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147042214X

ISBN 13

9781470422141

Material Geometry: Groupoids In Continuum Mechanics

By: Manuel De Leon,Marcelo Epstein,Victor Manuel Jimenez

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Material Geometry: Groupoids In Continuum Mechanics

By: Manuel De Leon,Marcelo Epstein,Victor Manuel Jimenez

This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.

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Page Count

226

Publisher

World Scientific

Published Date

ISBN 10

9811232563

ISBN 13

9789811232565

Supersymmetry and Equivariant de Rham Theory

By: Victor W Guillemin,Shlomo Sternberg

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Supersymmetry and Equivariant de Rham Theory

By: Victor W Guillemin,Shlomo Sternberg

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Page Count

243

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Springer Science & Business Media

Published Date

ISBN 10

3662039923

ISBN 13

9783662039922

Mathematics Past and Present Fourier Integral Operators

By: Jochen Brüning,Victor W Guillemin

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Mathematics Past and Present Fourier Integral Operators

By: Jochen Brüning,Victor W Guillemin

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Page Count

288

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Springer

Published Date

ISBN 10

3540567410

ISBN 13

9783540567417

Variations on a Theme by Kepler

By: Victor Guillemin,Shlomo Sternberg

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Variations on a Theme by Kepler

By: Victor Guillemin,Shlomo Sternberg

This book is based on the Colloquium Lectures presented by Shlomo Sternberg in 1990. The authors delve into the mysterious role that groups, especially Lie groups, play in revealing the laws of nature by focusing on the familiar example of Kepler motion: the motion of a planet under the attraction of the sun according to Kepler's laws. Newton realized that Kepler's second law--that equal areas are swept out in equal times--has to do with the fact that the force is directed radially to the sun. Kepler's second law is really the assertion of the conservation of angular momentum, reflecting the rotational symmetry of the system about the origin of the force. In today's language, we would say that the group $O(3)$ (the orthogonal group in three dimensions) is responsible for Kepler's second law. By the end of the nineteenth century, the inverse square law of attraction was seen to have $O(4)$ symmetry (where $O(4)$ acts on a portion of the six-dimensional phase space of the planet). Even larger groups h The remainder of the book is aimed at specialists. It begins with a demonstration that the Kepler problem and the hydrogen atom exhibit $O(4)$ symmetry and that the form of this symmetry determines the inverse square law in classical mechanics and the spectrum of the hydrogen atom in quantum mechanics. The space of regularized elliptical motions of the Kepler problem (also known as the Kepler manifold) plays a central role in this book. The last portion of the book studies the various cosmological models in this same conformal class (and having varying isometry groups) from the viewpoint of projective geometry. The computation of the hydrogen spectrum provides an illustration of the principle that enlarging the phase space can simplify the equations of motion in the classical setting and aid in the quantization problem in the quantum setting. The authors provide a short summary of the homological quantization of constraints and a list of recent applications to many interesting finite-dimensional set

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Publisher

American Mathematical Soc.

ISBN 10

0821869590

ISBN 13

9780821869598

Book's by Victor W Guillemin

Mathematics Past and Present Fourier Integral Operators

Mathematics Past and Present Fourier Integral Operators

Supersymmetry and Equivariant de Rham Theory

Supersymmetry and Equivariant de Rham Theory

Toric Topology

Toric Topology

Material Geometry: Groupoids In Continuum Mechanics

Material Geometry: Groupoids In Continuum Mechanics

Supersymmetry and Equivariant de Rham Theory

Supersymmetry and Equivariant de Rham Theory

Mathematics Past and Present Fourier Integral Operators

Mathematics Past and Present Fourier Integral Operators

Variations on a Theme by Kepler

Variations on a Theme by Kepler

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