Discrete Differential Geometry

Discrete Differential Geometry
Author: Alexander I. Bobenko
Publisher: American Mathematical Society
Total Pages: 432
Release: 2023-09-14
Genre: Mathematics
ISBN: 1470474565

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

Advances in Noncommutative Geometry
Author: Ali Chamseddine
Publisher: Springer Nature
Total Pages: 753
Release: 2020-01-13
Genre: Mathematics
ISBN: 3030295974

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.

Surveys on Recent Developments in Algebraic Geometry

Surveys on Recent Developments in Algebraic Geometry
Author: Izzet Coskun
Publisher: American Mathematical Soc.
Total Pages: 386
Release: 2017-07-12
Genre: Mathematics
ISBN: 1470435578

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.

Recent Advances in Algebraic Geometry

Recent Advances in Algebraic Geometry
Author: Christopher D. Hacon
Publisher: Cambridge University Press
Total Pages: 451
Release: 2015-01-15
Genre: Mathematics
ISBN: 110764755X

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

Advances in Architectural Geometry 2014

Advances in Architectural Geometry 2014
Author: Philippe Block
Publisher: Springer
Total Pages: 379
Release: 2014-12-26
Genre: Mathematics
ISBN: 3319114182

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.

Algorithmic Advances in Riemannian Geometry and Applications

Algorithmic Advances in Riemannian Geometry and Applications
Author: Hà Quang Minh
Publisher: Springer
Total Pages: 216
Release: 2016-10-05
Genre: Computers
ISBN: 3319450263

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 2010

Advances in Architectural Geometry 2010
Author: Cristiano Ceccato
Publisher: Birkhäuser
Total Pages: 242
Release: 2016-12-05
Genre: Technology & Engineering
ISBN: 3990433717

No detailed description available for "Advances in Architectural Geometry 2010".

Advances in Lorentzian Geometry

Advances in Lorentzian Geometry
Author: Matthias Plaue
Publisher: American Mathematical Soc.
Total Pages: 154
Release: 2011
Genre: Mathematics
ISBN: 082185352X

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 Algebraic Geometry Codes

Advances In Algebraic Geometry Codes
Author: Edgar Martinez-moro
Publisher: World Scientific
Total Pages: 453
Release: 2008-10-08
Genre: Mathematics
ISBN: 9814471615

Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.

Qα Analysis on Euclidean Spaces

Qα Analysis on Euclidean Spaces
Author: Jie Xiao
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 230
Release: 2019-03-18
Genre: Mathematics
ISBN: 3110600285

Starting with the fundamentals of Qα spaces and their relationships to Besov spaces, this book presents all major results around Qα spaces obtained in the past 16 years. The applications of Qα spaces in the study of the incompressible Navier-Stokes system and its stationary form are also discussed. This self-contained book can be used as an essential reference for researchers and graduates in analysis and partial differential equations.