Algebraic And Geometric Combinatorics On Lattice Polytopes
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Author |
: Takayuki Hibi |
Publisher |
: World Scientific |
Total Pages |
: 476 |
Release |
: 2019-05-30 |
ISBN-10 |
: 9789811200496 |
ISBN-13 |
: 9811200491 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes by : Takayuki Hibi
This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.
Author |
: Takayuki Hibi |
Publisher |
: World Scientific Publishing Company |
Total Pages |
: 0 |
Release |
: 2019 |
ISBN-10 |
: 9811200475 |
ISBN-13 |
: 9789811200472 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Algebraic and Geometric Combinatorics on Lattice Polytopes by : Takayuki Hibi
This volume consists of research papers and expository survey articles presented by the invited speakers of the workshop 'Algebraic and Geometric Combinatorics on Lattice Polytopes'. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further development of many research areas surrounding lattice polytopes. With the survey articles, research papers and open problems, graduate students can learn fundamental materials on lattice polytopes and researchers can find exciting activities and avenues for further exploration on lattice polytopes.
Author |
: Christos A. Athanasiadis |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 342 |
Release |
: 2006 |
ISBN-10 |
: 9780821840801 |
ISBN-13 |
: 0821840800 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Algebraic and Geometric Combinatorics by : Christos A. Athanasiadis
This volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.
Author |
: Rekha R. Thomas |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 156 |
Release |
: 2006 |
ISBN-10 |
: 0821841408 |
ISBN-13 |
: 9780821841402 |
Rating |
: 4/5 (08 Downloads) |
Synopsis Lectures in Geometric Combinatorics by : Rekha R. Thomas
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.
Author |
: Alexander M. Kasprzyk |
Publisher |
: Springer Nature |
Total Pages |
: 368 |
Release |
: 2022-06-08 |
ISBN-10 |
: 9783030983277 |
ISBN-13 |
: 3030983277 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Interactions with Lattice Polytopes by : Alexander M. Kasprzyk
This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.
Author |
: Günter Ewald |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 378 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461240440 |
ISBN-13 |
: 1461240441 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Combinatorial Convexity and Algebraic Geometry by : Günter Ewald
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.
Author |
: Hélène Barcelo |
Publisher |
: Springer |
Total Pages |
: 364 |
Release |
: 2019-01-21 |
ISBN-10 |
: 9783030051419 |
ISBN-13 |
: 3030051412 |
Rating |
: 4/5 (19 Downloads) |
Synopsis Recent Trends in Algebraic Combinatorics by : Hélène Barcelo
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
Author |
: Bruno Benedetti |
Publisher |
: Springer |
Total Pages |
: 222 |
Release |
: 2015-10-31 |
ISBN-10 |
: 9783319201559 |
ISBN-13 |
: 3319201557 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Combinatorial Methods in Topology and Algebra by : Bruno Benedetti
Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.
Author |
: William Fulton |
Publisher |
: Princeton University Press |
Total Pages |
: 174 |
Release |
: 1993 |
ISBN-10 |
: 0691000492 |
ISBN-13 |
: 9780691000497 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Introduction to Toric Varieties by : William Fulton
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.
Author |
: Ezra Miller |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 705 |
Release |
: 2007 |
ISBN-10 |
: 9780821837368 |
ISBN-13 |
: 0821837362 |
Rating |
: 4/5 (68 Downloads) |
Synopsis Geometric Combinatorics by : Ezra Miller
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.