Guillemin, Victor 1937
Overview
Works:  65 works in 449 publications in 4 languages and 7,911 library holdings 

Genres:  Educational films Documentary films Nonfiction films 
Roles:  Author, Editor, ed, Contributor 
Classifications:  QA613.6, 516.36 
Publication Timeline
.
Most widely held works about
Victor Guillemin
 Oral history interview with Linus Carl Pauling by Linus Pauling( )
 Guillemin, Victor W. : global analysis( )
Most widely held works by
Victor Guillemin
Differential topology by
Victor Guillemin(
Book
)
32 editions published between 1974 and 2014 in 3 languages and held by 827 WorldCat member libraries worldwide
32 editions published between 1974 and 2014 in 3 languages and held by 827 WorldCat member libraries worldwide
Measure theory and probability by
Malcolm Adams(
Book
)
28 editions published between 1986 and 1996 in English and held by 703 WorldCat member libraries worldwide
"Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. The measuretheoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on R [superscript n] (metric space approach), the BorelCantelli lemmas, straight measure theory (the Lebesgue integral). Chapter 3 expands on abstract Fourier analysis, Fourier series and the Fourier integral, which have some beautiful probabilistic applications: Polya's theorem on random walks, Kac's proof of the Szego theorem and the central limit theorem. In this concise text, quite a few applications to probability are packed into the exercises."Jacket
28 editions published between 1986 and 1996 in English and held by 703 WorldCat member libraries worldwide
"Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. The measuretheoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on R [superscript n] (metric space approach), the BorelCantelli lemmas, straight measure theory (the Lebesgue integral). Chapter 3 expands on abstract Fourier analysis, Fourier series and the Fourier integral, which have some beautiful probabilistic applications: Polya's theorem on random walks, Kac's proof of the Szego theorem and the central limit theorem. In this concise text, quite a few applications to probability are packed into the exercises."Jacket
Stable mappings and their singularities by
Martin Golubitsky(
Book
)
38 editions published between 1973 and 1986 in English and German and held by 657 WorldCat member libraries worldwide
38 editions published between 1973 and 1986 in English and German and held by 657 WorldCat member libraries worldwide
Symplectic techniques in physics by
Victor Guillemin(
Book
)
39 editions published between 1983 and 2011 in English and Undetermined and held by 641 WorldCat member libraries worldwide
39 editions published between 1983 and 2011 in English and Undetermined and held by 641 WorldCat member libraries worldwide
Geometric asymptotics by
Victor Guillemin(
Book
)
31 editions published between 1977 and 1991 in English and Undetermined and held by 515 WorldCat member libraries worldwide
31 editions published between 1977 and 1991 in English and Undetermined and held by 515 WorldCat member libraries worldwide
The spectral theory of Toeplitz operators by
L Boutet de Monvel(
Book
)
18 editions published between 1981 and 2016 in English and held by 464 WorldCat member libraries worldwide
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a selfadjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds
18 editions published between 1981 and 2016 in English and held by 464 WorldCat member libraries worldwide
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a selfadjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds
Seminar on microlocal analysis by
Victor Guillemin(
Book
)
18 editions published between 1979 and 2016 in English and Undetermined and held by 429 WorldCat member libraries worldwide
Based on a seminar sponsored by the Institute for Advanced Study in 19771978, this set of papers introduces microlocal analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups
18 editions published between 1979 and 2016 in English and Undetermined and held by 429 WorldCat member libraries worldwide
Based on a seminar sponsored by the Institute for Advanced Study in 19771978, this set of papers introduces microlocal analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups
Variations on a theme by Kepler by
Victor Guillemin(
Book
)
18 editions published between 1990 and 2006 in English and Undetermined and held by 412 WorldCat member libraries worldwide
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 lawthat equal areas are swept out in equal timeshas 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 rot
18 editions published between 1990 and 2006 in English and Undetermined and held by 412 WorldCat member libraries worldwide
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 lawthat equal areas are swept out in equal timeshas 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 rot
Cosmology in (2+1) dimensions, cyclic models, and deformations of M2,1 by
Victor Guillemin(
Book
)
18 editions published between 1988 and 2016 in English and Italian and held by 337 WorldCat member libraries worldwide
The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose lightlike geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "Floquet operator," invented by Paneitz and Segal
18 editions published between 1988 and 2016 in English and Italian and held by 337 WorldCat member libraries worldwide
The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose lightlike geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "Floquet operator," invented by Paneitz and Segal
Moment maps and combinatorial invariants of Hamiltonian Tn̳spaces by
Victor Guillemin(
Book
)
19 editions published between 1994 and 2013 in English and German and held by 308 WorldCat member libraries worldwide
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a oneone correspondence between certain types of moment polytopes and certain types of symplectic Gspaces. (One of the most challenging unsolved problems in symplectic geometry is to determine to what extent Delzants theorem is true of every compact symplectic GSpace.) The moment polytope also encodes quantum information about the actions of G. Using the methods of geometric quantization, one can frequently convert this action into a representations, p, of G on a Hilbert space, and in some sense the moment polytope is a diagrammatic picture of the irreducible representations of G which occur as subrepresentations of p. Precise versions of this item of folklore are discussed in Chapters 3 and 4. Also, midway through Chapter 2 a more complicated object is discussed: the DuistermaatHeckman measure, and the author explains in Chapter 4 how one can read off from this measure the approximate multiplicities with which the irreducible representations of G occur in p. This gives an excuse to touch on some results which are in themselves of great current interest: the DuistermaatHeckman theorem, the localization theorems in equivariant cohomology of AtiyahBott and BerlineVergne and the recent extremely exciting generalizations of these results by Witten, JeffreyKirwan, Lalkman, and others. The last two chapters of this book are a selfcontained and somewhat unorthodox treatment of the theory of toric varieties in which the usual hierarchal relation of complex to symplectic is reversed. This book is addressed to researchers and can be used as a semester text
19 editions published between 1994 and 2013 in English and German and held by 308 WorldCat member libraries worldwide
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a oneone correspondence between certain types of moment polytopes and certain types of symplectic Gspaces. (One of the most challenging unsolved problems in symplectic geometry is to determine to what extent Delzants theorem is true of every compact symplectic GSpace.) The moment polytope also encodes quantum information about the actions of G. Using the methods of geometric quantization, one can frequently convert this action into a representations, p, of G on a Hilbert space, and in some sense the moment polytope is a diagrammatic picture of the irreducible representations of G which occur as subrepresentations of p. Precise versions of this item of folklore are discussed in Chapters 3 and 4. Also, midway through Chapter 2 a more complicated object is discussed: the DuistermaatHeckman measure, and the author explains in Chapter 4 how one can read off from this measure the approximate multiplicities with which the irreducible representations of G occur in p. This gives an excuse to touch on some results which are in themselves of great current interest: the DuistermaatHeckman theorem, the localization theorems in equivariant cohomology of AtiyahBott and BerlineVergne and the recent extremely exciting generalizations of these results by Witten, JeffreyKirwan, Lalkman, and others. The last two chapters of this book are a selfcontained and somewhat unorthodox treatment of the theory of toric varieties in which the usual hierarchal relation of complex to symplectic is reversed. This book is addressed to researchers and can be used as a semester text
Supersymmetry and equivariant de Rham theory by
Victor Guillemin(
Book
)
14 editions published between 1999 and 2011 in English and held by 305 WorldCat member libraries worldwide
Equivariant cohomology in the framework of smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Brüning and V.M. Guillemin. The point of departure are two relatively short but very remarkable papers by Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie". These papers are reproduced here, together with a scholarly introduction to the subject from a modern point of view, written by two of the leading experts in the field. This "introduction", however, turns out to be a textbook of its own presenting the first full treatment of equivariant cohomology from the de Rahm theoretic perspective. The well established topological approach is linked with the differential form aspect through the equivariant de Rahm theorem. The systematic use of supersymmetry simplifies considerably the ensuing development of the basic technical tools which are then applied to a variety of subjects (like symplectic geometry, Lie theory, dynamical systems, and mathematical physics), leading up to the localization theorems and recent results on the ring structure of the equivariant cohomology
14 editions published between 1999 and 2011 in English and held by 305 WorldCat member libraries worldwide
Equivariant cohomology in the framework of smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Brüning and V.M. Guillemin. The point of departure are two relatively short but very remarkable papers by Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie". These papers are reproduced here, together with a scholarly introduction to the subject from a modern point of view, written by two of the leading experts in the field. This "introduction", however, turns out to be a textbook of its own presenting the first full treatment of equivariant cohomology from the de Rahm theoretic perspective. The well established topological approach is linked with the differential form aspect through the equivariant de Rahm theorem. The systematic use of supersymmetry simplifies considerably the ensuing development of the basic technical tools which are then applied to a variety of subjects (like symplectic geometry, Lie theory, dynamical systems, and mathematical physics), leading up to the localization theorems and recent results on the ring structure of the equivariant cohomology
Moment maps, cobordisms, and Hamiltonian group actions by
Victor Guillemin(
Book
)
12 editions published between 2000 and 2002 in English and held by 302 WorldCat member libraries worldwide
12 editions published between 2000 and 2002 in English and held by 302 WorldCat member libraries worldwide
Studies in applied mathematics : a volume dedicated to Irving Segal by
Victor Guillemin(
Book
)
17 editions published between 1978 and 1983 in 3 languages and held by 271 WorldCat member libraries worldwide
17 editions published between 1978 and 1983 in 3 languages and held by 271 WorldCat member libraries worldwide
Symplectic fibrations and multiplicity diagrams by
Victor Guillemin(
Book
)
14 editions published between 1996 and 2009 in English and held by 260 WorldCat member libraries worldwide
"The subject of this book is the multiplicity diagrams associated with U(n), O(n), and the other classical groups. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank2 and rank3 groups. The authors take a novel approach, using the techniques of symplectic geometry. They develop in detail some themes that were touched on in Symplectic Techniques in Physics (V. Guillemin and S. Sternberg, Cambridge University Press, 1984), including the geometry of the moment map, the DuistermaatHeckman theorem, the interplay between coadjoint orbits and representation theory, and quantization."
14 editions published between 1996 and 2009 in English and held by 260 WorldCat member libraries worldwide
"The subject of this book is the multiplicity diagrams associated with U(n), O(n), and the other classical groups. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank2 and rank3 groups. The authors take a novel approach, using the techniques of symplectic geometry. They develop in detail some themes that were touched on in Symplectic Techniques in Physics (V. Guillemin and S. Sternberg, Cambridge University Press, 1984), including the geometry of the moment map, the DuistermaatHeckman theorem, the interplay between coadjoint orbits and representation theory, and quantization."
Mathematics past and present : Fourier integral operators : selected classical articles by
J. J Duistermaat(
Book
)
13 editions published in 1994 in English and Undetermined and held by 210 WorldCat member libraries worldwide
13 editions published in 1994 in English and Undetermined and held by 210 WorldCat member libraries worldwide
Deformation theory of pseudogroup structures by
Victor Guillemin(
Book
)
13 editions published in 1966 in English and Italian and held by 200 WorldCat member libraries worldwide
13 editions published in 1966 in English and Italian and held by 200 WorldCat member libraries worldwide
Convexity properties of Hamiltonian group actions by
Victor Guillemin(
Book
)
10 editions published between 2005 and 2012 in English and held by 180 WorldCat member libraries worldwide
It reviews various infinitedimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel subgroup of a complex reductive group acing on a Kahler manifold, based on potentialtheoretic methods in several complex variables."Jacket
10 editions published between 2005 and 2012 in English and held by 180 WorldCat member libraries worldwide
It reviews various infinitedimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel subgroup of a complex reductive group acing on a Kahler manifold, based on potentialtheoretic methods in several complex variables."Jacket
Semiclassical analysis by
Victor Guillemin(
Book
)
6 editions published in 2013 in English and held by 41 WorldCat member libraries worldwide
6 editions published in 2013 in English and held by 41 WorldCat member libraries worldwide
Zoll surfaces by
Victor Guillemin(
Visual
)
5 editions published in 1986 in English and held by 22 WorldCat member libraries worldwide
Traces the idea of Zoll surfaces from its origin in the nineteenth century through the modern characterization using Riemann manifolds. Discusses recent developments in the spectral theory of Zoll manifolds
5 editions published in 1986 in English and held by 22 WorldCat member libraries worldwide
Traces the idea of Zoll surfaces from its origin in the nineteenth century through the modern characterization using Riemann manifolds. Discusses recent developments in the spectral theory of Zoll manifolds
Mathematics past and present : fourier integral operators by
Jochen Brüning(
)
2 editions published in 1994 in English and held by 0 WorldCat member libraries worldwide
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
2 editions published in 1994 in English and held by 0 WorldCat member libraries worldwide
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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Related Identities
 Sternberg, Shlomo Other Author Editor
 Pollack, Alan 1946
 Adams, Malcolm Ritchie Author
 Golubitsky, Martin 1945 Author
 Boutet de Monvel, L. 1941 Author
 Kashiwara, Masaki 1947 Contributor
 Kawai, Takahiro Contributor
 Kepler, Johannes 15711630
 Institute for Advanced Study (Princeton, N.J.)
 Karshon, Yael 1964
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Associated Subjects
Asymptotic expansions Cobordism theory Conformal geometry Convex domains Convex functions Convexity spaces Convex polytopes CosmologyMathematical models Diffeomorphisms Differentiable mappings Differential equations, Partial Differential topology Fourier integral operators Geometrical optics Geometric quantization Geometry, Differential Group theory Guillemin, Victor, Hamiltonian systems Homology theory Kepler, Johannes, Kepler's laws Lagrangian functions Lie groups Lorentz transformations Manifolds (Mathematics) Mappings (Mathematics) Mathematical analysis Mathematical physics Mathematics Matrices Measure theory Multiplicity (Mathematics) Planetary theory Probabilities Pseudogroups Pseudogroup structures, Deformation of Quantum theory Representations of groups Schrödinger operator Segal, Irving Ezra Singularities (Mathematics) Spectral theory (Mathematics) Supersymmetry Symmetry (Physics) Symplectic geometry Symplectic groups Symplectic manifolds Toeplitz operators Transformations (Mathematics)
Alternative Names
Giĭemin, V.
Gijemin, V.
Gijemin, V. 1937
Guillemin, V.
Guillemin, V. 1937
Guillemin, V. (Victor), 1937
Guillemin, V. W.
Guillemin, V. W. 1937
Guillemin, Victor
Guillemin, Victor 1937
Guillemin, Victor W.
Guillemin Victor W. 1937....
Guillemin, Victor William 1937
Victor Guillemin Amerikaans wiskundige
Victor Guillemin amerikansk matematikar
Victor Guillemin amerikansk matematiker
Victor Guillemin matemático estadounidense
Victor Guillemin matematico statunitense
Victor Guillemin mathématicien américain
Victor Guillemin USamerikanischer Mathematiker
Виктор Гийемин математик
Гийемин, B.
Гийемин, В 1937
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