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Lefschetz Properties And Enumerations
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Download or read book Lefschetz Properties written by Uwe Nagel and published by Springer Nature. This book was released on 2024 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds. Recent developments have demonstrated important cases of the Lefschetz property beyond the original geometric settings, such as Coxeter groups or matroids. Furthermore, there are connections to other branches of mathematics, for example, commutative algebra, algebraic topology, and combinatorics. Important results in this area have been obtained by finding unexpected connections between apparently different topics. A conference in Cortona, Italy in September 2022 brought together researchers discussing recent developments and working on new problems related to the Lefschetz properties. The book will feature surveys on several aspects of the theory as well as articles on new results and open problems.
Book Synopsis The Lefschetz Properties by : Tadahito Harima
Download or read book The Lefschetz Properties written by Tadahito Harima and published by Springer. This book was released on 2013-08-23 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
Book Synopsis Commutative Algebra by : Irena Peeva
Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume 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, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain 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.
Book Synopsis On the Shape of a Pure $O$-Sequence by : Mats Boij
Download or read book On the Shape of a Pure $O$-Sequence written by Mats Boij and published by American Mathematical Soc.. This book was released on 2012 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partial order is given by divisibility. If all, say t t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h_=(h0=1,h1,...,he), counting the monomials of X in each degree. Equivalently, pure O-sequences can be characterized as the f-vectors of pure multicomplexes, or, in the language of commutative algebra, as the h h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their f f-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences.
Book Synopsis Deformation of Artinian Algebras and Jordan Type by : Anthony Iarrobino
Download or read book Deformation of Artinian Algebras and Jordan Type written by Anthony Iarrobino and published by American Mathematical Society. This book was released on 2024-09-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18?22, 2022, at the Universit‚ Grenoble Alpes, Grenoble, France. Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case. Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry.
Book Synopsis Syzygies and Hilbert Functions by : Irena Peeva
Download or read book Syzygies and Hilbert Functions written by Irena Peeva and published by CRC Press. This book was released on 2007-03-20 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts.
Book Synopsis Vector Partitions, Visible Points and Ramanujan Functions by : Geoffrey B. Campbell
Download or read book Vector Partitions, Visible Points and Ramanujan Functions written by Geoffrey B. Campbell and published by CRC Press. This book was released on 2024-05-29 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector Partitions, Visible Points and Ramanujan Functions offers a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number theory and computational mathematics. It takes the reader up to research level, presenting new results alongside known classical results from integer partitions and areas of vector and multipartite partition theory. It also sets forth new directions for research for the more advanced reader. Above all, the intention of the book is to bring new inspiration to others who study mathematics and related areas. It is hoped that some new ideas will be launched to add value and insight into many of the classical and new theories surrounding partitions. The book is an appreciation of the many gifted authors of research into partitions over the past century and before, in the hope that more may come of this for future generations. Features Provides a step-by-step guide through the known literature on Integer and Vector Partitions, and a focus on the not so well-known Visible Point Vector identities Serves as a reference for graduate students and researchers in physics, applied mathematics, number theory and computational mathematics Offers a variety of practical examples as well as sets of exercises suitable for students and researchers Geoffrey B. Campbell completed his PhD at Australian National University in 1998 under the esteemed physicist Professor Rodney Baxter. His affiliation with the Australian National University Mathematical Sciences Institute has continued for over 30 years. Within that time frame, Geoffrey also served eight years as an Honorary Research Fellow at LaTrobe University Mathematics and Statistics Department in Melbourne. Currently he writes ongoing articles for the Australian Mathematical Society Gazette. Within the international scope, Geoffrey currently serves as a PhD external committee member for a mathematics graduate student at Washington State University in America. Geoffrey has built a career within Australian Commonwealth and State government departments, including as an Advisor at the Department of Prime Minister and Cabinet; as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.
Book Synopsis Surveys in Combinatorics 2021 by : Konrad K. Dabrowski
Download or read book Surveys in Combinatorics 2021 written by Konrad K. Dabrowski and published by Cambridge University Press. This book was released on 2021-06-24 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse–Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.
Book Synopsis Hodge Theory, Complex Geometry, and Representation Theory by : Robert S. Doran
Download or read book Hodge Theory, Complex Geometry, and Representation Theory written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2014 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains carefully written expository and research articles. Expository papers include discussions of Noether-Lefschetz theory, algebraicity of Hodge loci, and the representation theory of SL2(R). Research articles concern the Hodge conjecture, Harish-Chandra modules, mirror symmetry, Hodge representations of Q-algebraic groups, and compactifications, distributions, and quotients of period domains.
Book Synopsis The Mathematical Legacy of Richard P. Stanley by : Patricia Hersh
Download or read book The Mathematical Legacy of Richard P. Stanley written by Patricia Hersh and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.
Book Synopsis The Hilbert Function of a Level Algebra by : A. V. Geramita
Download or read book The Hilbert Function of a Level Algebra written by A. V. Geramita and published by American Mathematical Soc.. This book was released on 2007 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $R$ be a polynomial ring over an algebraically closed field and let $A$ be a standard graded Cohen-Macaulay quotient of $R$. The authors state that $A$ is a level algebra if the last module in the minimal free resolution of $A$ (as $R$-module) is of the form $R(-s)a$, where $s$ and $a$ are positive integers. When $a=1$ these are also known as Gorenstein algebras. The basic question addressed in this paper is: What can be the Hilbert Function of a level algebra? The authors consider the question in several particular cases, e.g., when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. The authors give new methods for showing that certain functions are NOT possible as the Hilbert function of a level algebra and also give new methods to construct level algebras. In a (rather long) appendix, the authors apply their results to give complete lists of all possible Hilbert functions in the case that the codimension of $A = 3$, $s$ is small and $a$ takes on certain fixed values.
Book Synopsis Applied Picard-Lefschetz Theory by : V. A. Vasilʹev
Download or read book Applied Picard-Lefschetz Theory written by V. A. Vasilʹev and published by American Mathematical Soc.. This book was released on 2002 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important functions of mathematical physics are defined as integrals depending on parameters. The Picard-Lefschetz theory studies how analytic and qualitative properties of such integrals (regularity, algebraicity, ramification, singular points, etc.) depend on the monodromy of corresponding integration cycles. In this book, V. A. Vassiliev presents several versions of the Picard-Lefschetz theory, including the classical local monodromy theory of singularities and completeintersections, Pham's generalized Picard-Lefschetz formulas, stratified Picard-Lefschetz theory, and also twisted versions of all these theories with applications to integrals of multivalued forms. The author also shows how these versions of the Picard-Lefschetz theory are used in studying a variety ofproblems arising in many areas of mathematics and mathematical physics. In particular, he discusses the following classes of functions: volume functions arising in the Archimedes-Newton problem of integrable bodies; Newton-Coulomb potentials; fundamental solutions of hyperbolic partial differential equations; multidimensional hypergeometric functions generalizing the classical Gauss hypergeometric integral. The book is geared toward a broad audience of graduate students, research mathematiciansand mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.
Book Synopsis Selected Works of Richard P. Stanley by : Victor Reiner
Download or read book Selected Works of Richard P. Stanley written by Victor Reiner and published by American Mathematical Soc.. This book was released on 2017-05-17 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1980 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Homological and Computational Methods in Commutative Algebra by : Aldo Conca
Download or read book Homological and Computational Methods in Commutative Algebra written by Aldo Conca and published by Springer. This book was released on 2017-11-16 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.
Book Synopsis Algebraic Curves and Projective Geometry by : Edoardo Ballico
Download or read book Algebraic Curves and Projective Geometry written by Edoardo Ballico and published by Springer. This book was released on 2006-11-14 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Queen's Papers in Pure and Applied Mathematics by : Queen's University (Kingston, Ont.)
Download or read book Queen's Papers in Pure and Applied Mathematics written by Queen's University (Kingston, Ont.) and published by . This book was released on 1966 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
