Convexity Properties Of Hamiltonian Group Actions
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Convexity Properties Of Hamiltonian Group Actions
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Author : Victor Guillemin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Convexity Properties Of Hamiltonian Group Actions written by Victor Guillemin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic" case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional 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 su This volume is recommended for independent study and is suitable for graduate students and researchers interested in symplectic geometry, algebraic geometry, and geometric combinatorics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.
Hamiltonian Group Actions And Equivariant Cohomology
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Author : Shubham Dwivedi
language : en
Publisher: Springer Nature
Release Date : 2019-09-23
Hamiltonian Group Actions And Equivariant Cohomology written by Shubham Dwivedi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-23 with Mathematics categories.
This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.
Convexity Of Singular Affine Structures And Toric Focus Integrable Hamiltonian Systems
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Author : Tudor S. Ratiu
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-31
Convexity Of Singular Affine Structures And Toric Focus Integrable Hamiltonian Systems written by Tudor S. Ratiu and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
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Poisson Geometry In Mathematics And Physics
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Author : Giuseppe Dito
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Poisson Geometry In Mathematics And Physics written by Giuseppe Dito and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.
Moment Maps Cobordisms And Hamiltonian Group Actions
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Author : Victor Guillemin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Moment Maps Cobordisms And Hamiltonian Group Actions written by Victor Guillemin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
Introduction To Symplectic Topology
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Author : Dusa McDuff
language : en
Publisher: Oxford University Press
Release Date : 2017-03-16
Introduction To Symplectic Topology written by Dusa McDuff and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.
Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.
Singularity Theory For Non Twist Kam Tori
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Author : A. González-Enríquez
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-08
Singularity Theory For Non Twist Kam Tori written by A. González-Enríquez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.
In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to non-twist invariant tori. Hence, bifurcating points correspond to non-twist tori.
Cocycles De Groupe Pour Mathrm Gl N Et Arrangements D Hyperplans
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Author : Nicolas Bergeron
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-10-16
Cocycles De Groupe Pour Mathrm Gl N Et Arrangements D Hyperplans written by Nicolas Bergeron and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-16 with Mathematics categories.
Ce livre constitue un exposé détaillé de la série de cours donnés en 2020 par le Prof. Nicolas Bergeron, titulaire de la Chaire Aisenstadt au CRM de Montréal. L'objet de ce texte est une ample généralisation d'une famille d'identités classiques, notamment la formule d'addition de la fonction cotangente ou celle des séries d'Eisenstein. Le livre relie ces identités à la cohomologie de certains sous-groupes arithmétiques du groupe linéaire général. Il rend explicite ces relations au moyen de la théorie des symboles modulaires de rang supérieur, dévoilant finalement un lien concret entre des objets de nature topologique et algébrique. This book provides a detailed exposition of the material presented in a series of lectures given in 2020 by Prof. Nicolas Bergeron while he held the Aisenstadt Chair at the CRM in Montréal. The topic is a broad generalization of certain classical identities such as the addition formulas for the cotangent function and for Eisenstein series. The book relates these identities to the cohomology of arithmetic subgroups of the general linear group. It shows that the relations can be made explicit using the theory of higher rank modular symbols, ultimately unveiling a concrete link between topological and algebraic objects. I think that the text “Cocycles de groupe pour $mathrm{GL}_n$ et arrangements d'hyperplans” is terrific. I like how it begins in a leisurely, enticing way with an elementary example that neatly gets to the topic. The construction of these “meromorphic function”-valued modular symbols are fundamental objects, and play (and will continue to play) an important role. —Barry Mazur, Harvard University
La Formule Des Traces Tordue D Apres Le Friday Morning Seminar
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Author : Jean-Pierre Labesse
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-03-07
La Formule Des Traces Tordue D Apres Le Friday Morning Seminar written by Jean-Pierre Labesse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.
La formule des traces pour un groupe reductif connexe arbitraire est due a James Arthur. Le cas tordu a fait l'objet du Friday Morning Seminar a l'Institute for Advanced Study de Princeton pendant l'annee academique 1983-1984. Lors de ce seminaire, des ex
The Geometric And Arithmetic Volume Of Shimura Varieties Of Orthogonal Type
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Author : Fritz Hörmann
language : en
Publisher: American Mathematical Society
Release Date : 2014-11-05
The Geometric And Arithmetic Volume Of Shimura Varieties Of Orthogonal Type written by Fritz Hörmann and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-05 with Mathematics categories.
This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.