Algebraic Geometry over the Complex Numbers

Author: Donu Arapura

Publisher: Springer Science & Business Media

ISBN: 1461418097

Category: Mathematics

Page: 329

View: 647

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
Posted in Mathematics

Topological Methods in Data Analysis and Visualization IV

Theory, Algorithms, and Applications

Author: Hamish Carr,Christoph Garth,Tino Weinkauf

Publisher: Springer

ISBN: 3319446843

Category: Mathematics

Page: 363

View: 2597

This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.
Posted in Mathematics

Real and Complex Singularities

Author: Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas

Publisher: American Mathematical Soc.

ISBN: 1470422050

Category: Differential geometry -- Classical differential geometry -- Classical differential geometry

Page: 355

View: 5414

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)
Posted in Differential geometry -- Classical differential geometry -- Classical differential geometry

Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology

Author: Stephan Mescher

Publisher: Springer

ISBN: 3319765841

Category: Mathematics

Page: 171

View: 1855

This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid’s approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
Posted in Mathematics

Holomorphic Curves in Low Dimensions

From Symplectic Ruled Surfaces to Planar Contact Manifolds

Author: Chris Wendl

Publisher: Springer

ISBN: 3319913719

Category: Mathematics

Page: 294

View: 1369

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Posted in Mathematics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1438

Posted in Mathematics

The Ricci Flow

Techniques and Applications

Author: N.A

Publisher: American Mathematical Soc.

ISBN: N.A

Category: Global differential geometry

Page: 517

View: 5571

Entropy, $\mu$-invariant, and finite time singularities Geometric tools and point picking methods Geometric properties of $\kappa$-solutions Compactness of the space of $\kappa$-solutions Perelman's pseudolocality theorem Tools used in proof of pseudolocality Heat kernel for static metrics Heat kernel for evolving metrics Estimates of the heat equation for evolving metrics Bounds for the heat kernel for evolving metrics Elementary aspects of metric geometry Convex functions on Riemannian manifolds Asymptotic cones and Sharafutdinov retraction Solutions to selected exercises Bibliography Index
Posted in Global differential geometry

Algebraic Models in Geometry

Author: Yves Félix,John Oprea,Daniel Tanré

Publisher: Oxford University Press on Demand

ISBN: 9780199206513

Category: Mathematics

Page: 460

View: 5115

In the past century, different branches of mathematics have become more widely separated. Yet, there is an essential unity to mathematics which still springs up in fascinating ways to solve interdisciplinary problems. This text provides a bridge between the subjects of algebraic topology, including differential topology, and geometry. It is a survey book dedicated to a large audience of researchers and graduate students in these areas. Containing a generalintroduction to the algebraic theory of rational homotopy and giving concrete applications of algebraic models to the study of geometrical problems, mathematicians in many areas will find subjects that are of interest to them in the book.
Posted in Mathematics

Geometry and Physics

XVI International Fall Workshop

Author: Rui Loja Fernandes,Roger Picken

Publisher: American Inst. of Physics

ISBN: 9780735405462

Category: Science

Page: 228

View: 9685

All papers have been peer-reviewed. The XVI International Fall Workshop on Geometry and Physics brought together geometers and physicists from within and outside the Iberian peninsula, to exchange ideas on how to describe and understand a variety of phenomena in areas such as mechanics or gravity.
Posted in Science

Asymptotic Analysis and Singularities―Hyperbolic and dispersive PDEs and fluid mechanics

Author: Hideo Kozono

Publisher: Amer Mathematical Society

ISBN: 9784931469402

Category: Mathematics

Page: 805

View: 5295

This volume is the proceedings of the 14th MSJ International Research Institute "Asymptotic Analysis and Singularity," which was held at Sendai, Japan in July 2005. The proceedings contain survey papers and original research papers on nonlinear partial differential equations, dynamical systems, calculus of variations and mathematical physics.
Posted in Mathematics

Geometry & Topology

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: N.A

View: 1851

Fully refereed international journal dealing with all aspects of geometry and topology and their applications.
Posted in Geometry

Mathematica Scandinavica

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6756

Posted in Mathematics

新收洋書総合目錄

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Catalogs, Union

Page: N.A

View: 4535

Posted in Catalogs, Union