Lie Groups And Geometric Aspects Of Isometric Actions

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Lie Groups and Geometric Aspects of Isometric Actions

Marcos M. Alexandrino,Renato G. Bettiol
Lie Groups and Geometric Aspects of Isometric Actions Book PDF

Author : Marcos M. Alexandrino,Renato G. Bettiol
Publisher : Springer
Page : 213 pages
File Size : 42,6 Mb
Release : 2015-05-22
Category : Mathematics
ISBN : 9783319166131

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Lie Groups and Geometric Aspects of Isometric Actions by Marcos M. Alexandrino,Renato G. Bettiol Pdf

This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.

Lie Group Actions in Complex Analysis

Dimitrij Akhiezer
Lie Group Actions in Complex Analysis Book PDF

Author : Dimitrij Akhiezer
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802675

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Lie Group Actions in Complex Analysis by Dimitrij Akhiezer Pdf

The main topic of this book is the sudy of the interaction between two major subjects of modern mathematics, namely, the theory of Lie groups with its specific methods and ways of thinking on the one hand and complex analysis with all its analytic, algebraic and geometric aspects. More specifically, the author concentrates on the double role of Lie groups in complex analysis, namely, as groups of biholomorphic self-made of certain complex analytic objects on the one hand and as a special class of complex manifolds with an additional strong structure on the other hand. The book starts from the basics of this subject and introduces the reader into many fields of recent research.

New Trends in Geometric Analysis

Antonio Alarcón,Vicente Palmer,César Rosales
New Trends in Geometric Analysis Book PDF

Author : Antonio Alarcón,Vicente Palmer,César Rosales
Publisher : Springer Nature
Page : 398 pages
File Size : 46,9 Mb
Release : 2023-11-25
Category : Mathematics
ISBN : 9783031399169

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New Trends in Geometric Analysis by Antonio Alarcón,Vicente Palmer,César Rosales Pdf

The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

Alfonso Zamora Saiz,Ronald A. Zúñiga-Rojas
Geometric Invariant Theory Holomorphic Vector Bundles and the Harder Narasimhan Filtration Book PDF

Author : Alfonso Zamora Saiz,Ronald A. Zúñiga-Rojas
Publisher : Springer Nature
Page : 127 pages
File Size : 40,9 Mb
Release : 2021-03-24
Category : Mathematics
ISBN : 9783030678296

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Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration by Alfonso Zamora Saiz,Ronald A. Zúñiga-Rojas Pdf

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.

Riemannian Manifolds and Homogeneous Geodesics

Valerii Berestovskii,Yurii Nikonorov
Riemannian Manifolds and Homogeneous Geodesics Book PDF

Author : Valerii Berestovskii,Yurii Nikonorov
Publisher : Springer Nature
Page : 482 pages
File Size : 51,6 Mb
Release : 2020-11-05
Category : Mathematics
ISBN : 9783030566586

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Riemannian Manifolds and Homogeneous Geodesics by Valerii Berestovskii,Yurii Nikonorov Pdf

This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.

Geometry, Rigidity, and Group Actions

Robert J. Zimmer,Benson Farb,David Fisher
Geometry Rigidity and Group Actions Book PDF

Author : Robert J. Zimmer,Benson Farb,David Fisher
Publisher : University of Chicago Press
Page : 659 pages
File Size : 44,7 Mb
Release : 2011-04-15
Category : Mathematics
ISBN : 9780226237893

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Geometry, Rigidity, and Group Actions by Robert J. Zimmer,Benson Farb,David Fisher Pdf

The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.

Mexican Mathematicians in the World

Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán
Mexican Mathematicians in the World Book PDF

Author : Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán
Publisher : American Mathematical Society
Page : 319 pages
File Size : 51,6 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9781470465360

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Mexican Mathematicians in the World by Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán Pdf

Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad (IV Reunión de Matemáticos Mexicanos en el Mundo), held from June 10–15, 2018, at Casa Matemática Oaxaca (CMO), Mexico. This meeting was the fourth in a series of ongoing biannual meetings bringing together Mexican mathematicians working abroad with their peers in Mexico. This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics, geometry, and topology. Their topics range from general relativity and mathematical physics to interactions between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on which the authors are currently working on, showcasing diverse research lines complementary to those currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches to well-known problems or new advances in active research fields.

System- and Data-Driven Methods and Algorithms

Peter Benner,et al.
System and Data Driven Methods and Algorithms Book PDF

Author : Peter Benner,et al.
Publisher : Walter de Gruyter GmbH & Co KG
Page : 346 pages
File Size : 45,8 Mb
Release : 2021-11-08
Category : Mathematics
ISBN : 9783110497717

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System- and Data-Driven Methods and Algorithms by Peter Benner,et al. Pdf

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.

Structure and Geometry of Lie Groups

Joachim Hilgert,Karl-Hermann Neeb
Structure and Geometry of Lie Groups Book PDF

Author : Joachim Hilgert,Karl-Hermann Neeb
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 55,6 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9780387847948

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Structure and Geometry of Lie Groups by Joachim Hilgert,Karl-Hermann Neeb Pdf

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.

Medical Image Computing and Computer Assisted Intervention – MICCAI 2019

Dinggang Shen,Tianming Liu,Terry M. Peters,Lawrence H. Staib,Caroline Essert,Sean Zhou,Pew-Thian Yap,Ali Khan
Medical Image Computing and Computer Assisted Intervention MICCAI 2019 Book PDF

Author : Dinggang Shen,Tianming Liu,Terry M. Peters,Lawrence H. Staib,Caroline Essert,Sean Zhou,Pew-Thian Yap,Ali Khan
Publisher : Springer Nature
Page : 809 pages
File Size : 46,9 Mb
Release : 2019-10-10
Category : Computers
ISBN : 9783030322519

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Medical Image Computing and Computer Assisted Intervention – MICCAI 2019 by Dinggang Shen,Tianming Liu,Terry M. Peters,Lawrence H. Staib,Caroline Essert,Sean Zhou,Pew-Thian Yap,Ali Khan Pdf

The six-volume set LNCS 11764, 11765, 11766, 11767, 11768, and 11769 constitutes the refereed proceedings of the 22nd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2019, held in Shenzhen, China, in October 2019. The 539 revised full papers presented were carefully reviewed and selected from 1730 submissions in a double-blind review process. The papers are organized in the following topical sections: Part I: optical imaging; endoscopy; microscopy. Part II: image segmentation; image registration; cardiovascular imaging; growth, development, atrophy and progression. Part III: neuroimage reconstruction and synthesis; neuroimage segmentation; diffusion weighted magnetic resonance imaging; functional neuroimaging (fMRI); miscellaneous neuroimaging. Part IV: shape; prediction; detection and localization; machine learning; computer-aided diagnosis; image reconstruction and synthesis. Part V: computer assisted interventions; MIC meets CAI. Part VI: computed tomography; X-ray imaging.

Geometry, Rigidity, and Group Actions

Robert J Zimmer
Geometry Rigidity and Group Actions Book PDF

Author : Robert J Zimmer
Publisher : University of Chicago Press
Page : 600 pages
File Size : 43,6 Mb
Release : 2011-04-15
Category : Mathematics
ISBN : 9780226237909

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Geometry, Rigidity, and Group Actions by Robert J Zimmer Pdf

The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.

Lie Groups and Lie Algebras I

V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Lie Groups and Lie Algebras I Book PDF

Author : V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 40,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642579998

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Lie Groups and Lie Algebras I by V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg Pdf

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Group Actions in Ergodic Theory, Geometry, and Topology

Robert J. Zimmer
Group Actions in Ergodic Theory Geometry and Topology Book PDF

Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 724 pages
File Size : 46,8 Mb
Release : 2019-12-23
Category : Mathematics
ISBN : 9780226568270

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Group Actions in Ergodic Theory, Geometry, and Topology by Robert J. Zimmer Pdf

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

Geometric Science of Information

Frank Nielsen,Frederic Barbaresco
Geometric Science of Information Book PDF

Author : Frank Nielsen,Frederic Barbaresco
Publisher : Springer
Page : 790 pages
File Size : 46,6 Mb
Release : 2015-10-24
Category : Computers
ISBN : 9783319250403

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Geometric Science of Information by Frank Nielsen,Frederic Barbaresco Pdf

This book constitutes the refereed proceedings of the Second International Conference on Geometric Science of Information, GSI 2015, held in Palaiseau, France, in October 2015. The 80 full papers presented were carefully reviewed and selected from 110 submissions and are organized into the following thematic sessions: Dimension reduction on Riemannian manifolds; optimal transport; optimal transport and applications in imagery/statistics; shape space and diffeomorphic mappings; random geometry/homology; Hessian information geometry; topological forms and Information; information geometry optimization; information geometry in image analysis; divergence geometry; optimization on manifold; Lie groups and geometric mechanics/thermodynamics; computational information geometry; Lie groups: novel statistical and computational frontiers; geometry of time series and linear dynamical systems; and Bayesian and information geometry for inverse problems.

Differential Geometry in the Large

Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner
Differential Geometry in the Large Book PDF

Author : Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner
Publisher : Cambridge University Press
Page : 401 pages
File Size : 45,7 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781108812818

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Differential Geometry in the Large by Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner Pdf

From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.