New Trends In Sub Riemannian Geometry
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New Trends In Sub Riemannian Geometry
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Author : Fabrice Baudoin
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-27
New Trends In Sub Riemannian Geometry written by Fabrice Baudoin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Mathematics categories.
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Sub-Riemannian Geometry and Interactions, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. Sub-Riemannian geometry is a generalization of Riemannian one, where a smooth metric is defined only on a preferred subset of tangent directions. Under the so-called Hörmander condition, all points are connected by finite-length curves, giving rise to a well-defined metric space. Sub-Riemannian geometry is nowadays a lively branch of mathematics, connected with probability, harmonic and complex analysis, subelliptic PDEs, geometric measure theory, optimal transport, calculus of variations, and potential analysis. The articles in this volume present some developments of a broad range of topics in sub-Riemannian geometry, including the theory of sub-elliptic operators, holonomy, spectral theory, and the geometry of the exponential map.
New Trends On Analysis And Geometry In Metric Spaces
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Author : Fabrice Baudoin
language : en
Publisher: Springer Nature
Release Date : 2022-02-04
New Trends On Analysis And Geometry In Metric Spaces written by Fabrice Baudoin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-04 with Mathematics categories.
This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.
New Trends In Geometric Analysis
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Author : Antonio Alarcón
language : en
Publisher: Springer Nature
Release Date : 2023-10-18
New Trends In Geometric Analysis written by Antonio Alarcón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-18 with Mathematics categories.
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.
Sub Riemannian Geometry
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Author : Andre Bellaiche
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Sub Riemannian Geometry written by Andre Bellaiche and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: control theory classical mechanics Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) diffusion on manifolds analysis of hypoelliptic operators Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: Andr Bellache: The tangent space in sub-Riemannian geometry Mikhael Gromov: Carnot-Carathodory spaces seen from within Richard Montgomery: Survey of singular geodesics Hctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers Jean-Michel Coron: Stabilization of controllable systems.
Recent Trends In Lorentzian Geometry
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Author : Miguel Sánchez
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Recent Trends In Lorentzian Geometry written by Miguel Sánchez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed. Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included. This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.
New Trends In Image Analysis And Processing Iciap 2017
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Author : Sebastiano Battiato
language : en
Publisher: Springer
Release Date : 2018-01-02
New Trends In Image Analysis And Processing Iciap 2017 written by Sebastiano Battiato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Computers categories.
This book constitutes the refereed proceedings of seven workshops held at the 19th International Conference on Image Analysis and Processing, ICIAP 2017, in Catania, Italy, in September 2017: First International Workshop on Brain-Inspired Computer Vision – WBICV 2017; Social Signal Processing and Beyond - SSPandBE 2017; Automatic affect analysis and synthesis - 3AS 2017; Background learning for detection and tracking from RGBD Videos - RGBD 2017; Natural human-computer Interaction and ecological perception in immersive Virtual and Augmented Reality - NIVAR 2017; 1st International Workshop on Biometrics as-a-service: cloud-based technology, systems and applications - IWBAAS 2017; 3rd International Workshop on Multimedia Assisted Dietary Management - MADiMa 2017.
From Representation Theory To Mathematical Physics And Back
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Author : Mikhail Khovanov
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-14
From Representation Theory To Mathematical Physics And Back written by Mikhail Khovanov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-14 with Mathematics categories.
This volume is a proceedings of a workshop at the Simons Center for Geometry and Physics from May 31– June 4, 2022. The workshop highlighted progress in the areas of vertex operator algebras, conformal field theory, categorification, low dimensional topology and representation theory of affine Lie algebras, loop groups, and quantum groups. In the past 40 years, string theory gave rise to the mathematical theory of vertex operator algebras, which led to the construction of representations of affine Lie algebras and the Moonshine module of the Monster group. These mathematical constructions have in turn led to ideas about 3-dimensional quantum gravity. In another direction, the discovery of the Jones polynomial led to a physical construction of 3-dimensional topological quantum field theories (TQFTs), which in turn advanced many mathematical developments in quantum groups and low dimensional topology. Louis Crane and Igor Frenkel introduced the categorification program with the goal of upgrading 3-dimensional TQFTs coming from representation theory of quantum groups to 4-dimensional TQFTs. This idea gave rise to the development of link homologies constructed from representation-theoretic, algebraic-geometric, combinatorial, and physical structures. Articles in this volume present both classical and new results related to these topics. They will be interesting to researchers and graduate students working in mathematical aspects of modern quantum field theory.
Regulators In Analysis Geometry And Number Theory
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Author : Alexander Reznikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Regulators In Analysis Geometry And Number Theory written by Alexander Reznikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is an outgrowth of the Workshop on "Regulators in Analysis, Geom etry and Number Theory" held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996. During the preparation and the holding of the workshop we were greatly helped by the director of the Landau Center: Lior Tsafriri during the time of the planning of the conference, and Hershel Farkas during the meeting itself. Organizing and running this workshop was a true pleasure, thanks to the expert technical help provided by the Landau Center in general, and by its secretary Simcha Kojman in particular. We would like to express our hearty thanks to all of them. However, the articles assembled in the present volume do not represent the proceedings of this workshop; neither could all contributors to the book make it to the meeting, nor do the contributions herein necessarily reflect talks given in Jerusalem. In the introduction, we outline our view of the theory to which this volume intends to contribute. The crucial objective of the present volume is to bring together concepts, methods, and results from analysis, differential as well as algebraic geometry, and number theory in order to work towards a deeper and more comprehensive understanding of regulators and secondary invariants. Our thanks go to all the participants of the workshop and authors of this volume. May the readers of this book enjoy and profit from the combination of mathematical ideas here documented.
Geometric Analysis And Applications To Quantum Field Theory
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Author : Peter Bouwknegt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Analysis And Applications To Quantum Field Theory written by Peter Bouwknegt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Geometry And Topology Of Aspherical Manifolds
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Author : Luca F. Di Cerbo
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-31
Geometry And Topology Of Aspherical Manifolds written by Luca F. Di Cerbo and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-31 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Singer–Hopf Conjecture in Geometry and Topology, held from March 18–19, 2023, at Georgia Institute of Technology, Atlanta, Georgia. It presents a multidisciplinary point of view on the Singer conjecture, the Hopf conjecture, the study on normalized Betti numbers, and several other intriguing questions on the fundamental group and cohomology of aspherical manifolds. This volume highlights many interesting research directions in the study of aspherical manifolds and covers a large collection of problems and conjectures about $L^2$-invariants of aspherical manifolds. It provides a snapshot of contemporary research in mathematics at the interface of geometry and topology, as well as algebraic geometry. The problems are presented from several distinct points of view, and the articles in this volume suggest possible generalizations and bridge a gap with closely related problems in differential geometry, complex algebraic geometry, and geometric topology. The volume can play a role in focusing the attention of the mathematical community on these fascinating problems which continue to resist the siege of geometers and topologists. It is our hope that this volume will become a valuable resource for early career mathematicians interested in these deep and important questions.