Algebraic

New mathematical research in arithmetic dynamicsIn The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional...

This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in...

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and...

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests...

This volume is an outcome of the conference 'Geometry and Foliations 2013' held in Tokyo in September 2013 and associated meetings, aimed for providing a good overview of the present studies as well as some perspective for further studies.The aspects and...

Equivariant cohomology has become an indispensable tool in algebraic geometry and in related areas including representation theory, combinatorial and enumerative geometry, and algebraic combinatorics. This text introduces the main ideas of the subject...

This volume is the proceedings of the online conference 'McKay correspondence, Mutation and Related Topics,' which was held at Kavli Institute for the Physics and Mathematics of the Universe (IPMU) in Japan in Summer in 2020.This volume consists of 15...

Algebraic geometry in a traditional and fast developing research area in east Asia. There were many world leading algebraic geometers and there are remarkably increasing active mathematicians in the related area in the East Asia area including China,...

The purpose of this book is twofold: to present some basic ideas in commutative algebra and algebraic geometry and to introduce some interesting topics of current research, centered around Grobner bases, resultants, and syzygies. The design of the text...

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties...

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum...

Measures and integralsBook InformationISBN 9780691095790Author John von NeumannFormat PaperbackPage Count 116Imprint Princeton University PressPublisher Princeton University PressWeight(grams) 255g

Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, Janos Kollar provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the...

This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in...

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of etale cohomology...

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by...

The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the...

In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how...

* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed...

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups...

Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area,...

Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. Their genesis and evolution are described in the preface as:Initially notes to...

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I...

Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be...

Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or...

From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the...

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Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning...

The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring...

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of...

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the...

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and...

Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems...

This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic Geometry in October 2004. Tropical Geometry ?rst appeared as a subject of its own in 2002, while its roots can be traced back at least to Bergman's work [1] on...

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning...

Let me begin with a little history. In the 20th century, algebraic geometry has gone through at least 3 distinct phases. In the period 1900-1930, largely under the leadership of the 3 Italians, Castelnuovo, Enriques and Severi, the subject grew immensely...

Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and...

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of...

Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi-Yau manifolds lies at an exciting intersection between...

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images.At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case...