Algebraic geometry

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them?

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry.

Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics.

Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems.

This book introduces the theory of modular forms with an eye toward the Modularity Theorem:All rational elliptic curves arise from modular forms.

He [Kronecker] was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number theory and alge- braic geometry as special cases.

The legacy of Galois was the beginning of Galois theory as well as group theory.

The aim of this book is to provide a guide to a rich and fascinating subject: algebraic curves, and how they vary in families.

to introduce these techniques and additional background is provided in appendices.

This text is intended to fill the gap between texts on classical algebraic geometry and the full-blown accounts of the theory of schemes.

This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University.

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study.

Oscar Zariski's work in mathematics permanently altered the foundations of algebraic geometry.

This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine 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.

There are three new appendices, one by Stefan Theisen on the role of Calabi- Yau manifolds in string theory and one by Otto Forster on the use of elliptic curves in computing theory and coding theory.

Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965.

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry.

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity.

In this modern treatment of the topic, Rolland Trapp presents an accessible introduction to the topic of multivariable calculus, supplemented by the use of fully interactive three-dimensional graphics throughout the text.

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

This book is a new edition of "e;Tensors and Manifolds: With Applications to Mechanics and Relativity"e; which was published in 1992.

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors.

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property.

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.

The theory of Riemann surfaces occupies a very special place in mathematics.

This edited collection of chapters, authored by leading experts, provides a complete and essentially self-contained construction of 3-fold and 4-fold klt flips.

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country.

Professor Atiyah is one of the greatest living mathematicians and is renowned in the mathematical world.

This comprehensive reference begins with a review of the basics followed by a presentation of flag varieties and finite- and infinite-dimensional representations in classical types and subvarieties of flag varieties and their singularities.

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology.

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 text presents a graduate-level introduction to differential geometry for mathematics and physics students.

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives.

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanta, Romania, on August 26-September 1, 2018.

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.

Trends in the Theory and Practice of Non-Linear Analysis

Introduction to Banach Spaces and their Geometry

Biomathematics in 1980

Real Elliptic Curves

Real Variable Methods in Fourier Analysis

Topics in Arithmetical Functions

Cohomology of Completions

An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics

Holomorphic Maps and Invariant Distances

Introduction to Algebraic Geometry and Algebraic Groups