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.
Author: Donu Arapura
Publisher: Springer Science & Business Media
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.
Theory, Algorithms, and Applications
Author: Hamish Carr,Christoph Garth,Tino Weinkauf
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)
Author: Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas
Publisher: American Mathematical Soc.
Category: Differential geometry -- Classical differential geometry -- Classical differential geometry
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
From Symplectic Ruled Surfaces to Planar Contact Manifolds
Author: Chris Wendl
Author: Edward Charles Keppelmann
Author: Norman Earl Steenrod,American Mathematical Society
Author: Ryan David Budney
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
Techniques and Applications
Publisher: American Mathematical Soc.
Category: Global differential geometry
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.
Author: Yves Félix,John Oprea,Daniel Tanré
Publisher: Oxford University Press on Demand
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.
XVI International Fall Workshop
Author: Rui Loja Fernandes,Roger Picken
Publisher: American Inst. of Physics
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.
Author: Hideo Kozono
Publisher: Amer Mathematical Society
Category: Catalogs, Union