Trends In Commutative Algebra
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Trends In Commutative Algebra
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Author : Luchezar L. Avramov
language : en
Publisher: Cambridge University Press
Release Date : 2004-12-13
Trends In Commutative Algebra written by Luchezar L. Avramov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-13 with Mathematics categories.
This book describes the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology, and combinatorics.
Current Developments In Algebraic Geometry
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Author : Lucia Caporaso
language : en
Publisher: Cambridge University Press
Release Date : 2012-03-19
Current Developments In Algebraic Geometry written by Lucia Caporaso and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-19 with Mathematics categories.
This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
Algebra Some Current Trends
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Author : Luchezar L. Avramov
language : en
Publisher: Springer
Release Date : 2006-11-14
Algebra Some Current Trends written by Luchezar L. Avramov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Current Trends On Monomial And Binomial Ideals
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Author : Huy Tài Hà
language : en
Publisher: MDPI
Release Date : 2020-03-18
Current Trends On Monomial And Binomial Ideals written by Huy Tài Hà and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-18 with Mathematics categories.
Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commutative algebra. The last ten years have seen a surge of research work in the study of monomial and binomial ideals. Remarkable developments in, for example, finite free resolutions, syzygies, Hilbert functions, toric rings, as well as cohomological invariants of ordinary powers, and symbolic powers of monomial and binomial ideals, have been brought forward. The theory of monomial and binomial ideals has many benefits from combinatorics and Göbner bases. Simultaneously, monomial and binomial ideals have created new and exciting aspects of combinatorics and Göbner bases. In the present Special Issue, particular attention was paid to monomial and binomial ideals arising from combinatorial objects including finite graphs, simplicial complexes, lattice polytopes, and finite partially ordered sets, because there is a rich and intimate relationship between algebraic properties and invariants of these classes of ideals and the combinatorial structures of their combinatorial counterparts. This volume gives a brief summary of recent achievements in this area of research. It will stimulate further research that encourages breakthroughs in the theory of monomial and binomial ideals. This volume provides graduate students with fundamental materials in this research area. Furthermore, it will help researchers find exciting activities and avenues for further exploration of monomial and binomial ideals. The editors express our thanks to the contributors to the Special Issue. Funds for APC (article processing charge) were partially supported by JSPS (Japan Society for the Promotion of Science) Grants-in-Aid for Scientific Research (S) entitled "The Birth of Modern Trends on Commutative Algebra and Convex Polytopes with Statistical and Computational Strategies" (JP 26220701). The publication of this volume is one of the main activities of the grant.
Developments And Trends In Infinite Dimensional Lie Theory
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Author : Karl-Hermann Neeb
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-17
Developments And Trends In Infinite Dimensional Lie Theory written by Karl-Hermann Neeb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-17 with Mathematics categories.
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Connections Between Algebra Combinatorics And Geometry
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Author : Susan M. Cooper
language : en
Publisher: Springer
Release Date : 2014-05-16
Connections Between Algebra Combinatorics And Geometry written by Susan M. Cooper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.
Monomial Ideals
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Author : Jürgen Herzog
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-28
Monomial Ideals written by Jürgen Herzog and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-28 with Mathematics categories.
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.
Ring And Module Theory
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Author : Toma Albu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Ring And Module Theory written by Toma Albu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.
This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
Recent Trends In Science And Technology Rtst 2023
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Author : Dr. Sr. Shanta Joseph, Dr. Usha Shukla, Dr. Pramod Yadaw, Mrs. Mamta Kashyap, Dr. W.B. Gurnule
language : en
Publisher: Shashwat Publication
Release Date : 2024-05-29
Recent Trends In Science And Technology Rtst 2023 written by Dr. Sr. Shanta Joseph, Dr. Usha Shukla, Dr. Pramod Yadaw, Mrs. Mamta Kashyap, Dr. W.B. Gurnule and has been published by Shashwat Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-29 with Biography & Autobiography categories.
International Seminar, Research Papers Proceeding on Recent Trends in Science and Technology (RTST-2023)
Trends In Optimization
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Author : American Mathematical Society. Short Course
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Trends In Optimization written by American Mathematical Society. Short Course and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). It focuses on seven exciting areas of discrete optimization. In particular, Karen Aardal describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction and H.W. Lenstra's use of this idea in the early 1980s in his polynomial-time algorithm for integer programming in fixed dimension. Aardal's article, lucid presentations of the material. It also contains practical developments using computational tools. Bernd Sturmfels' article, Algebraic recipes for integer programming, discusses how methods of commutative algebra and algebraic combinatorics can be used successfully to attack integer programming problems. Specifically, Grobner bases play a central role in algorithmic theory and practice. Moreover, it is shown that techniques based on short rational functions are bringing new insights, such as in computing the integer programming gap. Overall, these articles, together with five other contributions, make this volume an impressive compilation on the state-of-the-art of optimization. It is suitable for graduate students and researchers interested in discrete optimization.