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Geometric Invariant Theory And Decorated Principal Bundles
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Author :Alexander H. W. Schmitt Publisher :European Mathematical Society ISBN 13 :9783037190654 Total Pages :404 pages Book Rating :4.1/5 (96 download)
Book Synopsis Geometric Invariant Theory and Decorated Principal Bundles by : Alexander H. W. Schmitt
Download or read book Geometric Invariant Theory and Decorated Principal Bundles written by Alexander H. W. Schmitt and published by European Mathematical Society. This book was released on 2008 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.
Book Synopsis Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration by : Alfonso Zamora Saiz
Download or read book Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration written by Alfonso Zamora Saiz and published by Springer Nature. This book was released on 2021-03-24 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts
Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Book Synopsis Moduli Spaces and Vector Bundles by : Leticia Brambila-Paz
Download or read book Moduli Spaces and Vector Bundles written by Leticia Brambila-Paz and published by Cambridge University Press. This book was released on 2009-05-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
Book Synopsis Vector Bundles and Complex Geometry by : Oscar García-Prada
Download or read book Vector Bundles and Complex Geometry written by Oscar García-Prada and published by American Mathematical Soc.. This book was released on 2010 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers from the Conference on Vector Bundles held at Miraflores de la Sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, Hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.
Book Synopsis Lectures on Representations of Surface Groups by : François Labourie
Download or read book Lectures on Representations of Surface Groups written by François Labourie and published by . This book was released on 2013 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of these notes is the character variety of representations of a surface group in a Lie group. The author emphasizes the various points of view (combinatorial, differential, and algebraic) and is interested in the description of its smooth points, symplectic structure, volume and connected components. He also shows how a three manifold bounded by the surface leaves a trace in this character variety. These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In the first chapters, the author does not focus on the details of the differential geometric constructions and refers to classical textbooks, while in the more advanced chapters proofs occasionally are provided only for special cases where they convey the flavor of the general arguments. These notes might also be used by researchers entering this fast expanding field as motivation for further studies. The concluding paragraph of every chapter provides suggestions for further research.
Book Synopsis Invariant Manifolds and Dispersive Hamiltonian Evolution Equations by : Kenji Nakanishi
Download or read book Invariant Manifolds and Dispersive Hamiltonian Evolution Equations written by Kenji Nakanishi and published by European Mathematical Society. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.
Book Synopsis Geometric Numerical Integration and Schrödinger Equations by : Erwan Faou
Download or read book Geometric Numerical Integration and Schrödinger Equations written by Erwan Faou and published by European Mathematical Society. This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long periods of time. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long periods of time. In this setting, a natural question is how and to which extent the reproduction of such long-time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrodinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations are provided for them. The book grew out of a graduate-level course and is of interest to researchers and students seeking an introduction to the subject matter.
Book Synopsis Algebraic Cycles, Sheaves, Shtukas, and Moduli by : Piotr Pragacz
Download or read book Algebraic Cycles, Sheaves, Shtukas, and Moduli written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
Book Synopsis Moduli Spaces and Vector Bundles—New Trends by : Peter Gothen
Download or read book Moduli Spaces and Vector Bundles—New Trends written by Peter Gothen and published by American Mathematical Society. This book was released on 2024-07-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector Bundles—New Trends, held in honor of Peter Newstead's 80th birthday, from July 25–29, 2022, at the University of Warwick, Coventry, United Kingdom. The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory, Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research articles. Most articles contain substantial background and will be helpful to both novices and experts.
Book Synopsis String-Math 2014 by : Vincent Bouchard:
Download or read book String-Math 2014 written by Vincent Bouchard: and published by American Mathematical Soc.. This book was released on 2016-06-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference String-Math 2014 was held from June 9–13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: “String-Math Summer School” (held from June 2–6, 2014, at the University of British Columbia), “Calabi-Yau Manifolds and their Moduli” (held from June 14–18, 2014, at the University of Alberta), and “Quantum Curves and Quantum Knot Invariants” (held from June 16–20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.
Book Synopsis In the Tradition of Thurston II by : Ken’ichi Ohshika
Download or read book In the Tradition of Thurston II written by Ken’ichi Ohshika and published by Springer Nature. This book was released on 2022-08-02 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Book Synopsis Space – Time – Matter by : Jochen Brüning
Download or read book Space – Time – Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Book Synopsis Algebraic Geometry: Salt Lake City 2015 by : Tommaso de Fernex
Download or read book Algebraic Geometry: Salt Lake City 2015 written by Tommaso de Fernex and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.
Book Synopsis Moduli Spaces by : Leticia Brambila-Paz
Download or read book Moduli Spaces written by Leticia Brambila-Paz and published by Cambridge University Press. This book was released on 2014-03-13 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. First formalised in the 1960s, it represents a significant topic of modern mathematical research with strong connections to many areas of mathematics (including geometry, topology and number theory) and other disciplines such as theoretical physics. This book, which arose from a programme at the Isaac Newton Institute in Cambridge, is an ideal way for graduate students and more experienced researchers to become acquainted with the wealth of ideas and problems in moduli theory and related areas. The reader will find articles on both fundamental material and cutting-edge research topics, such as: algebraic stacks; BPS states and the P = W conjecture; stability conditions; derived differential geometry; and counting curves in algebraic varieties, all written by leading experts.
Book Synopsis Proceedings of the International Conference on Applied Sciences and Engineering (ICASE 2023) by : Ulziibayar Vandandoo
Download or read book Proceedings of the International Conference on Applied Sciences and Engineering (ICASE 2023) written by Ulziibayar Vandandoo and published by Springer Nature. This book was released on 2023-12-30 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an open access book. We kindly welcome to all academicians, researchers, scientists, engineers and graduate students in the related fields to submit their original research papers. Applications in engineering science that require expertise in mathematics, physics and chemistry. Its mission is to become a voice of the applied science community, addressing researchers and practitioners in different areas ranging from mathematics, physics, and chemistry to all related braches of the engineering, presenting verifiable computational methods, findings, and solutions. The Conference provided a setting for discussing recent developments in various engineering and applied science topics, including Mathematics, Chemistry, Physics, Computational science, Material science, Environmental Science and Chemical engineering. The submitted conference papers will be subjected to stringent peer review and carefully evaluated based on originality and clarity of exposition. All the accepted papers will be published in the conference proceedings. The conference provides opportunities for the attendants to share new ideas, experiences in Applied Sciences and Engineering and to establish collaboration for the future.
Book Synopsis From Quantum to Classical Molecular Dynamics by : Christian Lubich
Download or read book From Quantum to Classical Molecular Dynamics written by Christian Lubich and published by European Mathematical Society. This book was released on 2008 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations. This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrodinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized.
