Algebraic geometry

The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two.

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

Algorithms in algebraic geometry go hand in hand with software packages that implement them.

This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions.

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations.

An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds.

This volume contains three long lecture series by J.

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 "e;Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory"e;, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016.

This book is an introduction to singularities for graduate students and researchers.

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.

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.

This is the first book that focuses on practical algorithms for polynomial inequality proving and discovering.

This monograph presents a new model of mathematical structures called weak n-categories.

This textbook on homology and cohomology theory is geared towards the beginning graduate student.

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

The original goal that ultimately led to this volume was the construction of "e;motivic cohomology theory,"e; whose existence was conjectured by A.

Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices.

Plurisubharmonic functions playa major role in the theory of functions of several complex variables.

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions.

This is a volume of research articles related to finite groups.

Theta functions were studied extensively by Ramanujan.

This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field.

The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings.

Spectral Theory and Asymptotics of Differential Equations

The application of geometric algebra to the engineering sciences is a young, active subject of research.

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications.

The theory of complex analytic sets is part of the modern geometrical theory of functions of several complex variables.

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.

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "e;Lie Theory and Its Applications in Physics"e;, held near Varna, Bulgaria, in June 2015.

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.

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra.

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.

This monograph presents a new model of mathematical structures called weak n-categories.

This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

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

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field.

An introduction to Griffiths'' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

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

Introduction to Banach Spaces and their Geometry