Foliations 2012 - Proceedings Of The International Conference
Foliations 2012 - Proceedings Of The International Conference

Author: Jesus A Alvarez Lopez

Publisher: World Scientific

Published: 2013-10-25

Total Pages: 276

ISBN-13: 9814556874

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This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference “FOLIATIONS 2012”. It contains recent materials on foliation theory which is related to differential geometry, the theory of dynamical systems and differential topology. Both the original research and survey articles found in here should inspire students and researchers interested in foliation theory and the related fields to plan his/her further research.

Progress and Challenges in Dynamical Systems
Progress and Challenges in Dynamical Systems

Author: Santiago Ibáñez

Publisher: Springer Science & Business Media

Published: 2013-09-20

Total Pages: 426

ISBN-13: 3642388302

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This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.

Foliation Theory in Algebraic Geometry
Foliation Theory in Algebraic Geometry

Author: Paolo Cascini

Publisher: Springer

Published: 2016-03-30

Total Pages: 223

ISBN-13: 3319244604

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Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions. Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study./div

Introduction to Differential Geometry
Introduction to Differential Geometry

Author: Joel W. Robbin

Publisher: Springer Nature

Published: 2022-01-12

Total Pages: 426

ISBN-13: 3662643405

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This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.

Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology
Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

Author: Reiner Hermann:

Publisher: American Mathematical Soc.

Published: 2016-09-06

Total Pages: 158

ISBN-13: 1470419955

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In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Physiology of Elasmobranch Fishes: Structure and Interaction with Environment
Physiology of Elasmobranch Fishes: Structure and Interaction with Environment

Author: Robert E. Shadwick

Publisher: Academic Press

Published: 2015-11-16

Total Pages: 423

ISBN-13: 0128014431

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Fish Physiology: Physiology of Elasmobranch Fishes, Volume 34A is a useful reference for fish physiologists, biologists, ecologists, and conservation biologists. Following an increase in research on elasmobranchs due to the plight of sharks in today's oceans, this volume compares elasmobranchs to other groups of fish, highlights areas of interest for future research, and offers perspective on future problems. Covering measurements and lab-and-field based studies of large pelagic sharks, this volume is a natural addition to the renowned Fish Physiology series. - Provides needed comprehensive content on the physiology of elasmobranchs - Offers a systems approach between structure and interaction with the environment and internal physiology - Contains contributions by leading experts in their respective fields, under the guidance of internationally recognized and highly respected editors - Highlights areas of interest for future research, including perspective on future problems

Computer Vision – ECCV 2020
Computer Vision – ECCV 2020

Author: Andrea Vedaldi

Publisher: Springer Nature

Published: 2020-09-23

Total Pages: 501

ISBN-13: 3030585778

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The 30-volume set, comprising the LNCS books 12346 until 12375, constitutes the refereed proceedings of the 16th European Conference on Computer Vision, ECCV 2020, which was planned to be held in Glasgow, UK, during August 23-28, 2020. The conference was held virtually due to the COVID-19 pandemic. The 1360 revised papers presented in these proceedings were carefully reviewed and selected from a total of 5025 submissions. The papers deal with topics such as computer vision; machine learning; deep neural networks; reinforcement learning; object recognition; image classification; image processing; object detection; semantic segmentation; human pose estimation; 3d reconstruction; stereo vision; computational photography; neural networks; image coding; image reconstruction; object recognition; motion estimation.

Generic Coarse Geometry of Leaves
Generic Coarse Geometry of Leaves

Author: Jesús A. Álvarez López

Publisher: Springer

Published: 2018-07-28

Total Pages: 178

ISBN-13: 3319941321

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This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.