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Uhlenbeck Compactness
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Book Synopsis Uhlenbeck Compactness by : Katrin Wehrheim
Download or read book Uhlenbeck Compactness written by Katrin Wehrheim and published by European Mathematical Society. This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed account of the analytic foundations of gauge theory, namely, Uhlenbeck's compactness theorems for general connections and for Yang-Mills connections. It guides graduate students into the analysis of Yang-Mills theory as well as serves as a reference for researchers in the field. Largely self contained, the book contains a number of appendices (e.g., on Sobolev spaces of maps between manifolds) and an introductory part covering the $L^p$-regularity theory for the inhomogenous Neumann problem.
Book Synopsis Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields by : Yuan-Jen Chiang
Download or read book Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields written by Yuan-Jen Chiang and published by Springer Science & Business Media. This book was released on 2013-06-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.
Book Synopsis Gauge Theory and the Topology of Four-Manifolds by : Robert Friedman
Download or read book Gauge Theory and the Topology of Four-Manifolds written by Robert Friedman and published by American Mathematical Soc.. This book was released on 1998 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
Author :Daniel S. Freed Publisher :American Mathematical Society, IAS/Park City Mathematics Institute ISBN 13 :1470461234 Total Pages :476 pages Book Rating :4.4/5 (74 download)
Book Synopsis Quantum Field Theory and Manifold Invariants by : Daniel S. Freed
Download or read book Quantum Field Theory and Manifold Invariants written by Daniel S. Freed and published by American Mathematical Society, IAS/Park City Mathematics Institute. This book was released on 2021-12-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
Book Synopsis The Abel Prize 2018-2022 by : Helge Holden
Download or read book The Abel Prize 2018-2022 written by Helge Holden and published by Springer Nature. This book was released on 2024 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the winners of the Abel Prize in mathematics for the period 2018-2022: - Robert P. Langlands (2018) - Karen K. Uhlenbeck (2019) - Hillel Furstenberg and Gregory Margulis (2020) - Lászlo Lóvász and Avi Wigderson (2021) - Dennis P. Sullivan (2022) The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos from the period 2018-2022 showing many of the additional activities connected with the Abel Prize. This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer, 2014) as well as on The Abel Prize 2013-2017 (Springer, 2019), which profile the previous Abel Prize laureates.
Download or read book Modern Geometry written by Vicente Muñoz and published by American Mathematical Soc.. This book was released on 2018-09-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey articles of exciting new developments in geometry, written in tribute to Simon Donaldson to celebrate his 60th birthday. Reflecting the wide range of Donaldson's interests and influence, the papers range from algebraic geometry and topology through symplectic geometry and geometric analysis to mathematical physics. Their expository nature means the book acts as an invitation to the various topics described, while also giving a sense of the links between these different areas and the unity of modern geometry.
Book Synopsis A Course in Minimal Surfaces by : Tobias Holck Colding
Download or read book A Course in Minimal Surfaces written by Tobias Holck Colding and published by American Mathematical Society. This book was released on 2024-01-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
Book Synopsis Stochastic Analysis in Mathematical Physics by : Gerard Ben Arous
Download or read book Stochastic Analysis in Mathematical Physics written by Gerard Ben Arous and published by World Scientific. This book was released on 2008 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills theory and spin-glass theory.The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come.
Book Synopsis Stochastic Analysis In Mathematical Physics - Proceedings Of A Satellite Conference Of Icm 2006 by : Gerard Ben Arous
Download or read book Stochastic Analysis In Mathematical Physics - Proceedings Of A Satellite Conference Of Icm 2006 written by Gerard Ben Arous and published by World Scientific. This book was released on 2007-12-31 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills theory and spin-glass theory.The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come./a
Book Synopsis Complex and Symplectic Geometry by : Daniele Angella
Download or read book Complex and Symplectic Geometry written by Daniele Angella and published by Springer. This book was released on 2017-10-12 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Book Synopsis A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane by : Fabian Ziltener
Download or read book A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane written by Fabian Ziltener and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold . Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of to the Gromov-Witten theory of the symplectic quotient. The morphism should be a deformation of the Kirwan map. The idea, due to D. A. Salamon, is to define such a deformation by counting gauge equivalence classes of symplectic vortices over the complex plane . The present memoir is part of a project whose goal is to make this definition rigorous. Its main results deal with the symplectically aspherical case.
Book Synopsis Smooth Four-Manifolds and Complex Surfaces by : Robert Friedman
Download or read book Smooth Four-Manifolds and Complex Surfaces written by Robert Friedman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
Book Synopsis Concentration Compactness by : Kyril Tintarev
Download or read book Concentration Compactness written by Kyril Tintarev and published by Imperial College Press. This book was released on 2007 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
Book Synopsis Clifford Algebras by : Rafal Ablamowicz
Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.
Book Synopsis Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals by : Paul M Feehan
Download or read book Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals written by Paul M Feehan and published by American Mathematical Society. This book was released on 2021-02-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.
Book Synopsis Invariants of Homology 3-Spheres by : Nikolai Saveliev
Download or read book Invariants of Homology 3-Spheres written by Nikolai Saveliev and published by Springer Science & Business Media. This book was released on 2002-09-05 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.
Book Synopsis Geometry, Analysis and Probability by : Jean-Benoît Bost
Download or read book Geometry, Analysis and Probability written by Jean-Benoît Bost and published by Birkhäuser. This book was released on 2017-04-26 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
