Algebraic And Geometric Combinatorics On Lattice Polytopes
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Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes
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Author : Takayuki Hibi
language : en
Publisher: World Scientific
Release Date : 2019-05-30
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes written by Takayuki Hibi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-30 with Mathematics categories.
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.
Algebraic And Geometric Combinatorics On Lattice Polytopes
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Author : Hibi Takayuki
language : en
Publisher:
Release Date : 2019
Algebraic And Geometric Combinatorics On Lattice Polytopes written by Hibi Takayuki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with MATHEMATICS categories.
Algebraic And Geometric Combinatorics On Lattice Polytopes
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Author : Takayuki Hibi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2019
Algebraic And Geometric Combinatorics On Lattice Polytopes written by Takayuki Hibi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Polytopes categories.
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.
Algebraic And Geometric Combinatorics
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Author : Christos A. Athanasiadis
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Algebraic And Geometric Combinatorics written by Christos A. Athanasiadis 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 2006 with Mathematics categories.
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.
Combinatorial Convexity And Algebraic Geometry
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Author : Günter Ewald
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial Convexity And Algebraic Geometry written by Günter Ewald 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 2012-12-06 with Mathematics categories.
The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts.
Introduction To Toric Varieties
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Author : William Fulton
language : en
Publisher: Princeton University Press
Release Date : 1993
Introduction To Toric Varieties written by William Fulton and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
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.
Geometric Combinatorics
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Author : Ezra Miller
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Geometric Combinatorics written by Ezra Miller 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 2007 with Combinatorial analysis categories.
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.
Teaching Mathematics Through Games
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Author : Mindy Capaldi
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-05-18
Teaching Mathematics Through Games written by Mindy Capaldi 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 2021-05-18 with Education categories.
Active engagement is the key to learning. You want your students doing something that stimulates them to ask questions and creates a need to know. Teaching Mathematics Through Games presents a variety of classroom-tested exercises and activities that provoke the active learning and curiosity that you hope to promote. These games run the gamut from well-known favorites like SET and Settlers of Catan to original games involving simulating structural inequality in New York or playing Battleship with functions. The book contains activities suitable for a wide variety of college mathematics courses, including general education courses, math for elementary education, probability, calculus, linear algebra, history of math, and proof-based mathematics. Some chapter activities are short term, such as a drop-in lesson for a day, and some are longer, including semester-long projects. All have been tested, refined, and include extensive implementation notes.
Fourier Analysis On Polytopes And The Geometry Of Numbers
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Author : Sinai Robins
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-24
Fourier Analysis On Polytopes And The Geometry Of Numbers written by Sinai Robins and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.
This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.