Algebraic geometry

This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics.

In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli.

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

This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS).

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint.

This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers.

This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces.

This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday.

The Hardy-Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists.

This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets.

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

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.

Can artificial intelligence learn mathematics?

This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption.

This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras.

This book provides an overview of the latest progress on rationality questions in algebraic geometry.

This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field.

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry.

A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume.

This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples.

This volume introduces some recent developments in Arithmetic Geometry over local fields.

This book is an outgrowth of the conference "e;Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods"e; that was held in Paris in May 2016.

This book presents four lectures on Rees rings and blow-ups, Koszul modules with applications to syzygies, Grobner bases and degenerations, and applications of Adams operations.

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.

The goal of this book is to provide an introduction to algebraic geometry accessible to students.

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles.

The theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry.

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory.

This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes).

This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000.

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level.

Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied.

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

This book provides a rigorous and self-contained review of desingularization theory.

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory.

This book gives a modern presentation of modular operands and their role in string field theory.

This thesis proposes a new perspective on scattering amplitudes in quantum field theories.

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 book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmuller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018.

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity.

This book provides a comprehensive introduction to Soergel bimodules.

This book discusses regular powers and symbolic powers of ideals from three perspectives- algebra, combinatorics and geometry - and examines the interactions between them.

This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory.

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

This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves.

The textbook provides both beginner and experienced CAD users with the math behind the CAD.

This book gives a systematic presentation of real algebraic varieties.