Algebraic geometry

The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems.

The main goal of the CIME Summer School on "e;Algebraic Cycles and Hodge Theory"e; has been to gather the most active mathematicians in this area to make the point on the present state of the art.

Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm.

"e;Modular Forms with Integral and Half-Integral Weights"e; focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights.

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

The articles in this volume are devoted to:- moduli of coherent sheaves;- principal bundles and sheaves and their moduli;- new insights into Geometric Invariant Theory;- stacks of shtukas and their compactifications;- algebraic cycles vs.

This research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM).

This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces.

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K.

In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days.

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic.

This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K.

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering.

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.

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 book arose from a conference on "e;Singularities and Computer Algebra"e; which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday.

This volume contains articles related to the work of the Simons Collaboration "e;Arithmetic Geometry, Number Theory, and Computation.

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves.

Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers.

What is spectral action, how to compute it and what are the known examples?

Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry.

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1.

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors.

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Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage.

Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration.

The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry.

This book offers a non-standard introduction to quantum mechanics and quantum field theory, approaching these topics from algebraic and geometric perspectives.

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

Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples.

Locally semialgebraic spaces serve as an appropriateframework for studying the topological properties ofvarieties and semialgebraic sets over a real closed field.

This book is a remarkable contribution to the literature on dynamical systems and geometry.

The problem of enumerating maps (a map is a set of polygonal "e;countries"e; on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, .

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.

Automorphisms of Affine Spaces describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, Linearization and tame generators conjectures.

This volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel.

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 is a significant contribution within and across High Energy Physics and Algebraic Combinatorics.