Facets of Algebraic Geometry: Volume 2

Facets of Algebraic Geometry: Volume 2
Author: Paolo Aluffi
Publisher: Cambridge University Press
Total Pages: 396
Release: 2022-04-07
Genre: Mathematics
ISBN: 1108890547

Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

Facets of Algebraic Geometry: Volume 1

Facets of Algebraic Geometry: Volume 1
Author: Paolo Aluffi
Publisher: Cambridge University Press
Total Pages: 418
Release: 2022-04-07
Genre: Mathematics
ISBN: 1108890539

Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

Integrable Systems and Algebraic Geometry: Volume 2

Integrable Systems and Algebraic Geometry: Volume 2
Author: Ron Donagi
Publisher: Cambridge University Press
Total Pages: 537
Release: 2020-04-02
Genre: Mathematics
ISBN: 1108805337

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive second volume highlights the connections between her main fields of research, namely algebraic geometry and integrable systems. Written by leaders in the field, the text is accessible to graduate students and non-experts, as well as researchers.

Open Problems in Algebraic Combinatorics

Open Problems in Algebraic Combinatorics
Author: Christine Berkesch
Publisher: American Mathematical Society
Total Pages: 382
Release: 2024-08-21
Genre: Mathematics
ISBN: 147047333X

In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.

Mathematical Aspects of Quantum Field Theories

Mathematical Aspects of Quantum Field Theories
Author: Damien Calaque
Publisher: Springer
Total Pages: 572
Release: 2015-01-06
Genre: Science
ISBN: 3319099493

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Algebra, Geometry and Software Systems

Algebra, Geometry and Software Systems
Author: Michael Joswig
Publisher: Springer Science & Business Media
Total Pages: 332
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662051486

A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Using Algebraic Geometry

Using Algebraic Geometry
Author: David A Cox
Publisher: Springer Science & Business Media
Total Pages: 596
Release: 2005-03-17
Genre: Mathematics
ISBN: 9780387207339

The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.

C∞-Algebraic Geometry with Corners

C∞-Algebraic Geometry with Corners
Author: Kelli Francis-Staite
Publisher: Cambridge University Press
Total Pages: 224
Release: 2023-12-31
Genre: Mathematics
ISBN: 1009400207

Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.

Classical Algebraic Geometry

Classical Algebraic Geometry
Author: Igor V. Dolgachev
Publisher: Cambridge University Press
Total Pages: 653
Release: 2012-08-16
Genre: Mathematics
ISBN: 1139560786

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.