Multigraded Algebra And Applications

Author : Viviana Ene,Ezra Miller
Publisher : Springer
Page : 167 pages
File Size : 48,7 Mb
Release : 2018-06-08
Category : Mathematics
ISBN : 3319904922

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Multigraded Algebra and Applications by Viviana Ene,Ezra Miller Pdf

This volume contains research papers and surveys reflecting the topics discussed at the EMS Summer School on Multigraded Algebra and Applications held in Romania in August 2016. The school, which served as the 24th National School on Algebra, presented the main research directions of combinatorial commutative algebra with a strong focus on its applications in combinatorics, statistics, and biology. Recent progress in the field has led to new insights and suggested algebraic techniques for solving real-world data analysis problems. The summer school and resulting proceedings volume have raised numerous novel questions and encouraged a more interdisciplinary approach for young researchers when considering problems in pure and applied mathematical research. Featured topics in this volume include toric rings, binomial edge ideals, Betti numbers for numerical semigroup rings, and Waldschmidt constants. Researchers and graduate students interested in the developments of the field will find this book useful for their studies.

Author : Viviana Ene,Ezra Miller
Publisher : Springer
Page : 167 pages
File Size : 52,5 Mb
Release : 2018-06-07
Category : Mathematics
ISBN : 9783319904931

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Multigraded Algebra and Applications by Viviana Ene,Ezra Miller Pdf

This volume contains research papers and surveys reflecting the topics discussed at the EMS Summer School on Multigraded Algebra and Applications held in Romania in August 2016. The school, which served as the 24th National School on Algebra, presented the main research directions of combinatorial commutative algebra with a strong focus on its applications in combinatorics, statistics, and biology. Recent progress in the field has led to new insights and suggested algebraic techniques for solving real-world data analysis problems. The summer school and resulting proceedings volume have raised numerous novel questions and encouraged a more interdisciplinary approach for young researchers when considering problems in pure and applied mathematical research. Featured topics in this volume include toric rings, binomial edge ideals, Betti numbers for numerical semigroup rings, and Waldschmidt constants. Researchers and graduate students interested in the developments of the field will find this book useful for their studies.

Author : Syed Tariq Rizvi,Asma Ali,Vincenzo De Filippis
Publisher : Springer
Page : 430 pages
File Size : 45,8 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9789811016516

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Algebra and its Applications by Syed Tariq Rizvi,Asma Ali,Vincenzo De Filippis Pdf

This book discusses recent developments and the latest research in algebra and related topics. The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. Most of the papers were presented at the international conference on Algebra and its Applications (ICAA-2014), held at Aligarh Muslim University, India, from December 15–17, 2014. The book also includes papers from mathematicians who couldn't attend the conference. The conference has emerged as a powerful forum offering researchers a venue to meet and discuss advances in algebra and its applications, inspiring further research directions.

Author : Ezra Miller,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 41,5 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0387237070

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Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Pdf

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Author : Dumitru I. Stamate,Tomasz Szemberg
Publisher : Springer Nature
Page : 182 pages
File Size : 45,8 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030521110

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Combinatorial Structures in Algebra and Geometry by Dumitru I. Stamate,Tomasz Szemberg Pdf

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).

Author : Irena Peeva
Publisher : Springer Nature
Page : 898 pages
File Size : 50,9 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030896942

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Commutative Algebra by Irena Peeva Pdf

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. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra. The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 201 pages
File Size : 43,6 Mb
Release : 2013-08-24
Category : Mathematics
ISBN : 9783642387425

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Monomial Ideals, Computations and Applications by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Pdf

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Author : J Janyska,D Krupka
Publisher : World Scientific
Page : 480 pages
File Size : 53,7 Mb
Release : 1990-03-01
Category : Electronic
ISBN : 9789814611701

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Differential Geometry and Its Applications by J Janyska,D Krupka Pdf

The proceedings consists of lectures and selected original research papers presented at the conference. The contents is divided into 3 parts: I. Geometric structures, II. the calculus of variations on manifolds, III. Geometric methods in physics. The volume also covers interdisciplinary areas between differential geometry and mathematical physics like field theory, relativity, classical and quantum mechanics. Contents:On the Chern-Griffiths Formulas for an Upper Bound for the Rank of a Web (V V Goldberg)Natural and Gauge-Natural Operators on the Space of Linear Connections on a Vector Bundle (J Janyska)General Natural Bundles and Operators (I Kolár)Classes Caracteristiques Residuelles (D Lehmann)Remarks on Globalization of the Langrangian Formalism (A Borowiec)A Fresh Approach to the Poincaré-Cartan Form for a Linear PDE and a Map Between Cohomologies (T Harding & F J Bloore)Variational Sequences on Finite Order Jet Spaces (D Krupka)Equivalence of Degenerate Lagrangians of Higher Order (M de León & P R Rodrigues)Quantum SU(2) Group of Woronowicz and Poisson Structures (J Grabowski)Nonholonomic Intermediate Integrals of Partial Differential Equations (V V Lychagin & Yu R Romanovsky)The Metric in the Superspace of Riemannian Metrics and Its Relation to Gravity (H J Schmidt)Spherically Symmetric Vacuum Spacetimes: Global Approach (R Siegl)and others Readership: Mathematicians and mathematical physicists.

Author : David A. Cox Dinesh N. Manocha Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 43,5 Mb
Release : 2024-07-01
Category : Geometry, Algebraic
ISBN : 082186758X

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Applications of Computational Algebraic Geometry by David A. Cox Dinesh N. Manocha Bernd Sturmfels Pdf

Author : Paul C. Roberts
Publisher : Cambridge University Press
Page : 324 pages
File Size : 40,9 Mb
Release : 1998-05-13
Category : Mathematics
ISBN : 0521473160

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Multiplicities and Chern Classes in Local Algebra by Paul C. Roberts Pdf

Presents the theory of local Chern characters used in commutative algebra in an algebraic setting.

Author : V. M. Buchstaber,Taras E. Panov
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 41,8 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821831861

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Torus Actions and Their Applications in Topology and Combinatorics by V. M. Buchstaber,Taras E. Panov Pdf

Here, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a propermanifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements. This approachalso provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatoricsand will help to establish even tighter connections between the subjects involved.

Author : Roger Howe,Markus Hunziker,Jeb F. Willenbring
Publisher : Springer
Page : 562 pages
File Size : 45,7 Mb
Release : 2015-01-04
Category : Mathematics
ISBN : 9781493915903

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Symmetry: Representation Theory and Its Applications by Roger Howe,Markus Hunziker,Jeb F. Willenbring Pdf

Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.

Author : Aron Simis,Zaqueu Ramos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 464 pages
File Size : 42,9 Mb
Release : 2022-03-21
Category : Mathematics
ISBN : 9783110640694

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Graded Algebras in Algebraic Geometry by Aron Simis,Zaqueu Ramos Pdf

The objective of this book is to look at certain commutative graded algebras that appear frequently in algebraic geometry. By studying classical constructions from geometry from the point of view of modern commutative algebra, this carefully-written book is a valuable source of information, offering a careful algebraic systematization and treatment of the problems at hand, and contributing to the study of the original geometric questions.

Author : Sultan Catto,Alvany Rocha
Publisher : World Scientific
Page : 1228 pages
File Size : 45,7 Mb
Release : 1992-01-27
Category : Electronic
ISBN : 9789814555500

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Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes) by Sultan Catto,Alvany Rocha Pdf

This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research.The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.

Author : B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401152587

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Lie Groups and Lie Algebras by B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky Pdf

This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.