Algebraic geometry

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces.

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics.

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.

Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results.

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions.

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics.

This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master's and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics.

This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University.

This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018.

This proceedings volume covers a range of research topics in algebra from the Southern Regional Algebra Conference (SRAC) that took place in March 2017.

This volume collects contributions from speakers at the INdAM Workshop "e;Birational Geometry and Moduli Spaces"e;, which was held in Rome on 11-15 June 2018.

The objective of this book is to provide tools for solving problems which involve cubic number fields.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants of the workshop "e;Positivity and Valuations"e;, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 22nd to 26th, 2016.

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

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.

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve.

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc.

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

This book arises from the INdAM Meeting "e;Complex and Symplectic Geometry"e;, which was held in Cortona in June 2016.

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

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

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

This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties.

This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry.

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 unique collection of new and classical problems provides full coverage of geometric inequalities.

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015.

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

This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics.

This collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it.

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 examines the life and work of mathematician Giovanni Battista Guccia, founder of the Circolo Matematico di Palermo and its renowned journal, the Rendiconti del Circolo matematico di Palermo.

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.

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).

The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painleve equations, and it offers new results on a particular Painleve III equation of type PIII (D6), called PIII (0, 0, 4, -4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections.

This unique collection of new and classical problems provides full coverage of algebraic inequalities.

This advanced textbook provides a comprehensive and unified account of the moment problem.

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "e;Automorphic Forms and L-Functions"e;, held at the University of Heidelberg in 2016.

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

This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties.

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

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

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 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 .

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

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.

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.