Algebraic geometry

Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Grobner bases) and geometry (via quiver theory).

This unique collection of new and classical problems provides full coverage of algebraic inequalities.

This book provides a systematic account of several breakthroughs in the modern theory of zeta functions.

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997.

This volume presents a panorama of the diverse activities organized by V.

We investigate GIT quotients of polarized curves.

Matched Asymptotic Expansions and Singular Perturbations

Spherical buildings are certain combinatorial simplicial complexes intro- duced, at first in the language of "e;incidence geometries,"e; to provide a sys- tematic geometric interpretation of the exceptional complex Lie groups.

This second edition has been completely restructured, resulting in a compelling description of vector analysis from its first appearance as a byproduct of Hamilton's quaternions to the use of vectors in solving geometric problems.

The second of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research.

Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa- tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang- Mills connections.

This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry.

This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems.

The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series.

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes.

This book is an extended and revised version of "e;Numerical Semigroups with Applications,"e; published by Springer as part of the RSME series.

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc.

Holomorphic Functions, Domains of Holomorphy and Local Properties

Surveys and articles on recent developments in pure and applied singularity theory.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

A systematic exposition of the basics of period domains.

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi-Yau varieties and string theory.

Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics.

This volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend.

This unique collection of new and classical problems provides full coverage of geometric inequalities.

This book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022.

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points.

The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry.

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

This book starts with a concise but rigorous overview of the basic notions of projective geometry, using straightforward and modern language.

This third volume of four describes all the most important techniques, mainly based on Gröbner bases.

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type.

Trends in the Theory and Practice of Non-Linear Analysis

Explains both the how and the why of linear algebra to get students thinking like mathematicians.

This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems.

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry.

Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures.

This book presents a new and innovative approach to Lie groups and differential geometry.