Part of Cambridge Texts in Applied Mathematics
Publication planned for: January 2019
format: Hardback
isbn: 9781108419390
format: Paperback
isbn: 9781108410892
Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.
Establishes a trajectory from basic combinatorial and simplicial topology all the way to persistent homology
Illustrates numerous established techniques with thorough treatment
This book has been classroom tested, and written by distinguished researchers of international stature
Part I. Topological Preliminaries:
1. Topological spaces
2. Simplicial complexes
Part II. Delaunay Complexes:
3. Convex polytopes
4. Delaunay complexes
5. Good triangulations
6. Delaunay filtrations
Part III. Reconstruction of Smooth Submanifolds:
7. Triangulation of submanifolds
8. Reconstruction of submanifolds
Part IV. Distance-Based Inference:
9. Stability of distance functions
10. Distance to probability measures
11. Homology inference.
Part of Cambridge Monographs on Mathematical Physics
Publication planned for: October 2018
format: Hardback
isbn: 9781108429917
Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.
Covers a wide range of topological solitons including self-dual solitons and compactons
Discussion focuses on classical scalar field theory making the book compact and coherent
Integrable and non-integrable scalar field theories are considered providing a single viewpoint on different non-linear systems
Preface
Part I. Kinks and Solitary Waves:
1. Sine-Gordon model
2. Kinks in the models with polynomial potentials
3. Non-topological solitons: Korteweg-de-Vries system
Part II. O(3) Sigma Model, Lumps and Baby Skyrmions:
4. O(3) Non-linear sigma model
5. Baby skyrmions
Part III. Q-balls, Skyrmions and Hopfions:
6. Q-balls
7. Skyrmions
8. Hopfions
References
Index.
Part of New Mathematical Monographs
Publication planned for: November 2018
format: Hardback
isbn: 9781108425810
Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a uniform way for all groups. Prominent examples include stable homotopy, K-theory or bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible actions of all compact Lie groups. This book introduces graduate students and researchers to global equivariant homotopy theory. The framework is based on the new notion of global equivalences for orthogonal spectra, a much finer notion of equivalence than is traditionally considered. The treatment is largely self-contained and contains many examples, making it suitable as a textbook for an advanced graduate class. At the same time, the book is a comprehensive research monograph with detailed calculations that reveal the intrinsic beauty of global equivariant phenomena.
Contains full proofs of many fundamental properties that are hard to find in the literature
Readers will gain a deeper understanding by working through the many examples
Suitable as a complete reference and as a standard textbook on the subject
1. Unstable global homotopy theory
2. Ultra-commutative monoids
3. Equivariant stable homotopy theory
4. Global stable homotopy theory
5. Ultra-commutative ring spectra
6. Global Thom and K-theory spectra
Appendix A. Compactly generated spaces
Appendix B. Equivariant spaces
Appendix C. Enriched functor categories
Bibliography
Symbol Index
Index.
Part of London Mathematical Society Lecture Note Series
Publication planned for: January 2019
format: Paperback
isbn: 9781108431637
Description
In this edited volume leaders in the field of partial differential equations present recent work on topics in PDEs arising from geometry and physics. The papers originate from a 2015 research school organized by CIMPA and MIMS in Hammamet, Tunisia to celebrate the 60th birthday of the late Professor Abbas Bahri. The opening chapter commemorates his life and work. While the research presented in this book is cutting-edge, the treatment throughout is at a level accessible to graduate students. It includes short courses offering readers a unique opportunity to learn the state of the art in evolution equations and mathematical models in physics, which will serve as an introduction for students and a useful reference for established researchers. Finally, the volume includes many open problems to inspire the next generation.
Covers the state of the art in partial differential equations
Presents an excellent graduate-level overview covering a variety of topics related to PDEs
Authored by leading specialists in the field
Preface Mohamed Ben Ayed, Mohamed Ali Jendoubi, Yomna Rebai, Hassna Riahi and Hatem Zaag
Abbas Bahri: a dedicated life Mohamed Ben Ayed
1. Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension Asma Azaiez, Nader Masmoudi and Hatem Zaag
2. On the role of anisotropy in the weak stability of the Navier?Stokes system Hajer Bahouri, Jean-Yves Chemin and Isabelle Gallagher
3. The motion law of fronts for scalar reaction-diffusion equations with multiple wells: the degenerate case Fabrice Bethuel and Didier Smets
4. Finite-time blowup for some nonlinear complex Ginzburg?Landau equations Thierry Cazenave and Seifeddine Snoussi
5. Asymptotic analysis for the Lane?Emden problem in dimension two Francesca de Marchis, Isabella Ianni and Filomena Pacella
6. A data assimilation algorithm: the paradigm of the 3D Leray-ƒ¿ model of turbulence Aseel Farhat, Evelyn Lunasin and Edriss S. Titi
7. Critical points at infinity methods in CR geometry Najoua Gamara
8. Some simple problems for the next generations Alain Haraux
9. Clustering phenomena for linear perturbation of the Yamabe equation Angela Pistoia and Giusi Vaira
10. Towards better mathematical models for physics Luc Tartar.
Hardback
August 10, 2018 Forthcoming by CRC Press
Reference - 219 Pages - 55 B/W Illustrations
ISBN 9781138065499 - CAT# K33398
*Written to be a self-contained treatment of Gorenstein homological algebra
*Gives an up-to-date presentation of the subject
*Includes an overview of some of the main open problems in Gorenstein homological algebra, and discusses the current status in solving them
*Incorporates research-level material, as well as a review of basic results from homological and commutative algebra
*Discusses the connections between Gorenstein homological algebra and Tate (co)homology
Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications
Foreword
Preface
1 Modules - projective, injective, at modules
2 Gorenstein projective, injective and at modules
3 Gorenstein projective resolutions
4 Gorenstein injective resolutions
5 Gorenstein at precovers and preenvelopes
6 Connections with Tate (co)homology
7 Totally acyclic complexes
8 Generalizations of the Gorenstein modules
9 Gorenstein projective, injective, at complexes, dg-projective, dg-injective, dg-at complexes