Algebraic geometry

This book is a collection of the lectures and talks presented in the Tohoku Forum for Creativity in the thematic year 2015 'Fundamental Problems in Quantum Physics: Strings, Black Holes and Quantum Information', and related events in the period 2014-2016.

Absolute values and their completions -like the p-adic number fields- play an important role in number theory.

It is gratifying that this textbook is still sufficiently popular to warrant a third edition.

This textbook offers a thorough, modern introduction into commutative algebra.

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.

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems.

This is a monograph about non-commutative algebraic geometry, and its application to physics.

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices.

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.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

This detailed exposition makes classical algebraic geometry accessible to the modern mathematician.

This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry.

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

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

Number theory is a branch of mathematics which draws its vitality from a rich historical background.

This book is essential reading for anyone interested in low-dimensional topology.

The collection of papers in this volume represents recent advances in the under- standing of the geometry and topology of singularities.

This English translation of Daniel Coray's original French textbook Notes de geometrie et d'arithmetique introduces students to Diophantine geometry.

I am pleased to participate in this Summer School and look forward to sharing some ideas with you over the next few days.

[From the foreword by B.

This book constitutes the proceedings of the 2000 Howard conference on "e;Infinite Dimensional Lie Groups in Geometry and Representation Theory"e;.

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry.

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups.

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.

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions.

Algebraic geometry has its origin in the study of systems of polynomial equations f (x ,.

This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere.

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory.

This book explores determinantal ideals of square matrices from the perspective of commutative algebra, with a particular emphasis on linear matrices.

This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry.

Bornologies and Functional Analysis

This book serves as an illuminating introduction to the intricacies of the geometry of numbers.

From its birth (in Babylon?

To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000.

The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra.

This book explores determinantal ideals of square matrices from the perspective of commutative algebra, with a particular emphasis on linear matrices.

This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory.

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

This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary.

The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics.

A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.

This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting "e;Homological and Computational Methods in Commutative Algebra"e; held in Cortona (Italy) from May 30 to June 3, 2016 .