Algebraic geometry

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 is the revised second edition of the well-received book by the first two authors.

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.

MATRIX is Australia's international and residential mathematical research institute.

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.

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 book presents a unified mathematical treatment of diverse problems in thegeneral domain of robotics and associated fields using Clifford or geometric alge-bra.

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.

The primary aim of this monograph is to achieve part of Beilinson's program on mixed motives using Voevodsky's theories of A1-homotopy and motivic complexes.

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

The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites.

This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators.

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

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout.

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 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 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.

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

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.

This volume is an outcome of the workshop "e;Moduli of K-stable Varieties"e;, which was held in Rome, Italy in 2017.

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

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

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

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

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.

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

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

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

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.

This book is built upon a basic second-year masters course given in 1991- 1992, 1992-1993 and 1993-1994 at the Universit' e Paris-Sud (Orsay).

Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations.

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.

The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups.

Enumerative geometry is a core area of algebraic geometry that dates back to Apollonius in the second century BCE.

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable).

In preparing this monograph I had three objectives.

This textbook is intended for a course in algebraic topology at the beginning graduate level.

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties.

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016.

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties.

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi-Yau varieties and string theory.

This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.

Nolan Wallach's mathematical research is remarkable in both its breadth and depth.

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems.

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction.

The elements of abstract algebra have almost everywhere found a place in the undergraduate courses of universities, but this has happened to some extent at the expense of courses on geometry.