Advances In Geometry

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Discrete Differential Geometry

Alexander I. Bobenko,Yuri B. Suris
Discrete Differential Geometry Book PDF

Author : Alexander I. Bobenko,Yuri B. Suris
Publisher : American Mathematical Society
Page : 432 pages
File Size : 40,5 Mb
Release : 2023-09-14
Category : Mathematics
ISBN : 9781470474560

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Discrete Differential Geometry by Alexander I. Bobenko,Yuri B. Suris Pdf

An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

Advances in Noncommutative Geometry

Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu
Advances in Noncommutative Geometry Book PDF

Author : Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu
Publisher : Springer Nature
Page : 753 pages
File Size : 51,5 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 9783030295974

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Advances in Noncommutative Geometry by Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu Pdf

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Advances in Geometry

Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor
Advances in Geometry Book PDF

Author : Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217701

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Advances in Geometry by Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor Pdf

This book is an outgrowth of the activities of the Center for Geometry and Mathematical Physics (CGMP) at Penn State from 1996 to 1998. The Center was created in the Mathematics Department at Penn State in the fall of 1996 for the purpose of promoting and supporting the activities of researchers and students in and around geometry and physics at the university. The CGMP brings many visitors to Penn State and has ties with other research groups; it organizes weekly seminars as well as annual workshops The book contains 17 contributed articles on current research topics in a variety of fields: symplectic geometry, quantization, quantum groups, algebraic geometry, algebraic groups and invariant theory, and character istic classes. Most of the 20 authors have talked at Penn State about their research. Their articles present new results or discuss interesting perspec tives on recent work. All the articles have been refereed in the regular fashion of excellent scientific journals. Symplectic geometry, quantization and quantum groups is one main theme of the book. Several authors study deformation quantization. As tashkevich generalizes Karabegov's deformation quantization of Kahler manifolds to symplectic manifolds admitting two transverse polarizations, and studies the moment map in the case of semisimple coadjoint orbits. Bieliavsky constructs an explicit star-product on holonomy reducible sym metric coadjoint orbits of a simple Lie group, and he shows how to con struct a star-representation which has interesting holomorphic properties.

Recent Advances in Algebraic Geometry

Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Recent Advances in Algebraic Geometry Book PDF

Author : Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Publisher : Cambridge University Press
Page : 451 pages
File Size : 50,8 Mb
Release : 2015-01-15
Category : Mathematics
ISBN : 9781107647558

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Recent Advances in Algebraic Geometry by Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa Pdf

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Surveys on Recent Developments in Algebraic Geometry

Izzet Coskun,Tommaso de Fernex,Angela Gibney
Surveys on Recent Developments in Algebraic Geometry Book PDF

Author : Izzet Coskun,Tommaso de Fernex,Angela Gibney
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 43,6 Mb
Release : 2017-07-12
Category : $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions
ISBN : 9781470435578

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Surveys on Recent Developments in Algebraic Geometry by Izzet Coskun,Tommaso de Fernex,Angela Gibney Pdf

The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

Algorithmic Advances in Riemannian Geometry and Applications

Hà Quang Minh,Vittorio Murino
Algorithmic Advances in Riemannian Geometry and Applications Book PDF

Author : Hà Quang Minh,Vittorio Murino
Publisher : Springer
Page : 208 pages
File Size : 46,5 Mb
Release : 2016-10-05
Category : Computers
ISBN : 9783319450261

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Algorithmic Advances in Riemannian Geometry and Applications by Hà Quang Minh,Vittorio Murino Pdf

This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.

Advances in Architectural Geometry 2014

Philippe Block,Jan Knippers,Niloy J. Mitra,Wenping Wang
Advances in Architectural Geometry 2014 Book PDF

Author : Philippe Block,Jan Knippers,Niloy J. Mitra,Wenping Wang
Publisher : Springer
Page : 379 pages
File Size : 50,9 Mb
Release : 2014-12-26
Category : Mathematics
ISBN : 9783319114187

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Advances in Architectural Geometry 2014 by Philippe Block,Jan Knippers,Niloy J. Mitra,Wenping Wang Pdf

This book contains 24 technical papers presented at the fourth edition of the Advances in Architectural Geometry conference, AAG 2014, held in London, England, September 2014. It offers engineers, mathematicians, designers, and contractors insight into the efficient design, analysis, and manufacture of complex shapes, which will help open up new horizons for architecture. The book examines geometric aspects involved in architectural design, ranging from initial conception to final fabrication. It focuses on four key topics: applied geometry, architecture, computational design, and also practice in the form of case studies. In addition, the book also features algorithms, proposed implementation, experimental results, and illustrations. Overall, the book presents both theoretical and practical work linked to new geometrical developments in architecture. It gathers the diverse components of the contemporary architectural tendencies that push the building envelope towards free form in order to respond to multiple current design challenges. With its introduction of novel computational algorithms and tools, this book will prove an ideal resource to both newcomers to the field as well as advanced practitioners.

Advances in Lorentzian Geometry

Matthias Plaue,Alan D. Rendall,Mike Scherfner
Advances in Lorentzian Geometry Book PDF

Author : Matthias Plaue,Alan D. Rendall,Mike Scherfner
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 53,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853528

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Advances in Lorentzian Geometry by Matthias Plaue,Alan D. Rendall,Mike Scherfner Pdf

Offers insight into the methods and concepts of a very active field of mathematics that has many connections with physics. It includes contributions from specialists in differential geometry and mathematical physics, collectively demonstrating the wide range of applications of Lorentzian geometry, and ranging in character from research papers to surveys to the development of new ideas.

Advances in Algebra and Geometry

C. Musili
Advances in Algebra and Geometry Book PDF

Author : C. Musili
Publisher : Springer
Page : 311 pages
File Size : 44,6 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9789386279125

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Advances in Algebra and Geometry by C. Musili Pdf

Contributed articles presented at the Conference, sponsored by National Science Foundation, USA [and others].

Algebraic Geometry Codes: Advanced Chapters

Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin
Algebraic Geometry Codes Advanced Chapters Book PDF

Author : Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin
Publisher : American Mathematical Soc.
Page : 453 pages
File Size : 40,9 Mb
Release : 2019-07-02
Category : Coding theory
ISBN : 9781470448653

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Algebraic Geometry Codes: Advanced Chapters by Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin Pdf

Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.

SAGA – Advances in ShApes, Geometry, and Algebra

Tor Dokken,Georg Muntingh
SAGA Advances in ShApes Geometry and Algebra Book PDF

Author : Tor Dokken,Georg Muntingh
Publisher : Springer
Page : 323 pages
File Size : 48,6 Mb
Release : 2014-10-24
Category : Mathematics
ISBN : 9783319086354

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SAGA – Advances in ShApes, Geometry, and Algebra by Tor Dokken,Georg Muntingh Pdf

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

Semidefinite Optimization and Convex Algebraic Geometry

Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas
Semidefinite Optimization and Convex Algebraic Geometry Book PDF

Author : Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas
Publisher : SIAM
Page : 487 pages
File Size : 48,7 Mb
Release : 2013-03-21
Category : Mathematics
ISBN : 9781611972283

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Semidefinite Optimization and Convex Algebraic Geometry by Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas Pdf

An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Advances in Architectural Geometry 2016

Sigrid Adriaenssens,Fabio Gramazio,Matthias Kohler,Achim Menges,Mark Pauly
Advances in Architectural Geometry 2016 Book PDF

Author : Sigrid Adriaenssens,Fabio Gramazio,Matthias Kohler,Achim Menges,Mark Pauly
Publisher : vdf Hochschulverlag AG
Page : 408 pages
File Size : 45,7 Mb
Release : 2016-09-09
Category : Architectural design
ISBN : 9783728137777

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Advances in Architectural Geometry 2016 by Sigrid Adriaenssens,Fabio Gramazio,Matthias Kohler,Achim Menges,Mark Pauly Pdf

The Advances in Architectural Geometry (AAG) symposia serve as a unique forum where developments in the design, analysis and fabrication of building geometry are presented. With participation of both academics and professionals, each symposium aims to gather and present practical work and theoretical research that responds to contemporary design challenges and expands the opportunities for architectural form. The fifth edition of the AAG symposia was hosted by the National Centre for Competence in Research Digital Fabrication at ETH Zurich, Switzerland, in September 2016. This book contains the proceedings from the AAG2016 conference and offers detailed insight into current and novel geometrical developments in architecture. The 22 diverse, peer-reviewed papers present cutting-edge innovations in the fields of mathematics, computer graphics, software design, structural engineering, and the design and construction of architecture.

Introduction to Algebraic Geometry

Serge Lang
Introduction to Algebraic Geometry Book PDF

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 46,8 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9780486839806

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Introduction to Algebraic Geometry by Serge Lang Pdf

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Lectures on the Geometry of Poisson Manifolds

Izu Vaisman
Lectures on the Geometry of Poisson Manifolds Book PDF

Author : Izu Vaisman
Publisher : Birkhäuser
Page : 210 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884952

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Lectures on the Geometry of Poisson Manifolds by Izu Vaisman Pdf

This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.