Interactions With Lattice Polytopes

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Interactions with Lattice Polytopes

Author : Alexander M. Kasprzyk
Publisher : Springer Nature
ISBN 13 : 3030983277
Total Pages : 368 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Interactions with Lattice Polytopes by : Alexander M. Kasprzyk

Download or read book Interactions with Lattice Polytopes written by Alexander M. Kasprzyk and published by Springer Nature. This book was released on 2022-06-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Polytopes, Rings, and K-Theory

Author : Winfried Bruns
Publisher : Springer Science & Business Media
ISBN 13 : 0387763562
Total Pages : 461 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Polytopes, Rings, and K-Theory by : Winfried Bruns

Download or read book Polytopes, Rings, and K-Theory written by Winfried Bruns and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.

Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes

Author : Takayuki Hibi
Publisher : World Scientific
ISBN 13 : 9811200491
Total Pages : 476 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes by : Takayuki Hibi

Download or read book Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes written by Takayuki Hibi and published by World Scientific. This book was released on 2019-05-30 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory

Author : Abhijit Champanerkar
Publisher : American Mathematical Soc.
ISBN 13 : 0821849603
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory by : Abhijit Champanerkar

Download or read book Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory written by Abhijit Champanerkar and published by American Mathematical Soc.. This book was released on 2011 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.

Computing the Continuous Discretely

Author : Matthias Beck
Publisher : Springer
ISBN 13 : 1493929690
Total Pages : 295 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Computing the Continuous Discretely by : Matthias Beck

Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

Existence of Unimodular Triangulations–Positive Results

Author : Christian Haase
Publisher : American Mathematical Soc.
ISBN 13 : 1470447169
Total Pages : 83 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Existence of Unimodular Triangulations–Positive Results by : Christian Haase

Download or read book Existence of Unimodular Triangulations–Positive Results written by Christian Haase and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.

Fundamental Interactions

Author : Daniel Grumiller
Publisher : World Scientific
ISBN 13 : 9814277835
Total Pages : 422 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Fundamental Interactions by : Daniel Grumiller

Download or read book Fundamental Interactions written by Daniel Grumiller and published by World Scientific. This book was released on 2010 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memorial volume on the work of Wolfgang Kummer brings together articles devoted to the history of high energy physics with detailed coverage on the scientific concepts and scientific institutions, in particular CERN OCo and the underlying physics involved. Covering recent advances and developments as well as giving a reminiscent overview in two rapidly evolving fields of high energy/particle physics, and gravitational physics, the commemorative volume contains more than 20 original invited paper contributions OCo which will appear for the first time in print OCo from eminent and renowned physicists who interacted and collaborated with Wolfgang Kummer, including Physics Nobel Laureate Jack Steinberger. Wolfgang Kummer was president of the CERN council from 1985 to 1987, among his numerous eminent academic and administrative positions which he held during his illustrious career. This volume also aims to demonstrate and highlight Wolfgang Kummer''s significant contribution to the foundational work in gauge field theory, particle physics, and quantum gravity, and the tremendous impact leading to cutting-edge findings and advances at LHC. Sample Chapter(s). Foreword (155 KB). Chapter 1: Noncovariant Gauges at Zero and Nonzero Temperature (215 KB). Contents: Gauge Field Theory and Particle Physics: Noncovariant Gauges at Zero and Nonzero Temperature (P V Landshoff); Non-Relativistic Bound States: The Long Way Back from the BetheOCoSalpeter to the SchrAdinger Equation (A Vairo); Distended/Diminished Topologically Massive Electrodynamics (S Deser); Dynamical Spin (P G O Freund); Quantum Corrections to Solitons and BPS Saturation (A Rebhan et al.); Gauging Noncommutative Theories (H Grosse & M Wohlgenannt); Topological Phases and Contextuality Effects in Neutron Quantum Optics (H Rauch); First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-Form (M Hansen & T Strobl); Some Local and Global Aspects of the Gauge Fixing in YangOCoMills-Theories (D N Blaschke et al.); Frozen Ghosts in Thermal Gauge Field Theory (P V Landshoff & A Rebhan); Classical and Quantum Gravity: Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity (L Bergamin & R Meyer); Order and Chaos in Two Dimensional Gravity (R B Mann); 2-D Midisuperspace Models for Quantum Black Holes (J Gegenberg & G Kunstatter); Global Solutions in Gravity. Euclidean Signature (M O Katanaev); Thoughts on the Cosmological Principle (D J Schwarz); When Time Emerges (C Faustmann et al.); Towards Noncommutative Gravity (D V Vassilevich); Superembedding Approach to Superstring in AdS 5 X S 5 Superspace (I A Bandos); Heterotic (0,2) Gepner Models and Related Geometries (M Kreuzer); Canonical Analysis of Cosmological Topologically Massive Gravity at the Chiral Point (D Grumiller et al.); Wolfgang Kummer and the Physics Community: Wolfgang Kummer at CERN (H Schopper); Wolfgang Kummer and the Little Lost Lane Boy (K Lane); Mitigation of Fossil Fuel Consumption and Global Warming by Thermal Solar Electric Power Production in the World''s Deserts (J Steinberger); (My) Life with Wolfgang Kummer (M Schweda); Schubert in Stony Brook and Kinks in Vienna (P van Nieuwenhuizen). Readership: Scientists, researchers, graduates and undergraduates interested in high energy, particle or gravitational physics."

Interactions of Classical and Numerical Algebraic Geometry

Author : Daniel James Bates
Publisher : American Mathematical Soc.
ISBN 13 : 0821847465
Total Pages : 379 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Interactions of Classical and Numerical Algebraic Geometry by : Daniel James Bates

Download or read book Interactions of Classical and Numerical Algebraic Geometry written by Daniel James Bates and published by American Mathematical Soc.. This book was released on 2009-09-16 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1351645919
Total Pages : 2354 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 2354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Combinatorial Commutative Algebra

Author : Ezra Miller
Publisher : Springer Science & Business Media
ISBN 13 : 0387271031
Total Pages : 425 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Combinatorial Commutative Algebra by : Ezra Miller

Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-11-13 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Quantum Interaction

Author : Harald Atmanspacher
Publisher : Springer
ISBN 13 : 3319286757
Total Pages : 293 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Quantum Interaction by : Harald Atmanspacher

Download or read book Quantum Interaction written by Harald Atmanspacher and published by Springer. This book was released on 2016-01-07 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Quantum Interaction, QI 2015, held in Filzbach, Switzerland, in July 2015. The 20 papers together with 2 invited keynotes presented in this book were carefully selected from 27 submissions. Quantum Interaction has developed into an emerging interdisciplinary area of science combining research topics in mathematics, physics, psychology, economics, cognitive science, and computer science.

Computational Oriented Matroids

Author : Jürgen Bokowski
Publisher : Cambridge University Press
ISBN 13 : 0521849306
Total Pages : 294 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Computational Oriented Matroids by : Jürgen Bokowski

Download or read book Computational Oriented Matroids written by Jürgen Bokowski and published by Cambridge University Press. This book was released on 2006-05-08 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The variety of applications corresponds to the variety of ways they can be defined. Each of these definitions corresponds to a differing data structure for an oriented matroid, and handling them requires computational support, best realised through a functional language. Haskell is used here, and, for the benefit of readers, the book includes a primer on it. The combination of concrete applications and computation, the profusion of illustrations, many in colour, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Triangulations

Author : Jesus De Loera
Publisher : Springer Science & Business Media
ISBN 13 : 3642129714
Total Pages : 547 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Triangulations by : Jesus De Loera

Download or read book Triangulations written by Jesus De Loera and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.

Convexity from the Geometric Point of View

Author : Vitor Balestro
Publisher : Springer Nature
ISBN 13 : 3031505077
Total Pages : 1195 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Convexity from the Geometric Point of View by : Vitor Balestro

Download or read book Convexity from the Geometric Point of View written by Vitor Balestro and published by Springer Nature. This book was released on with total page 1195 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn

Author : Michel-marie Deza
Publisher : World Scientific
ISBN 13 : 1783260866
Total Pages : 186 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn by : Michel-marie Deza

Download or read book Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn written by Michel-marie Deza and published by World Scientific. This book was released on 2004-02-13 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph identifies polytopes that are “combinatorially ℓ1-embeddable”, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to “ℓ2-prominent” affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability — the main unifying question, to which those lists are subjected — is presented with the minimum of technicalities.

Outer Billiards on Kites

Author : Richard Evan Schwartz
Publisher : Princeton University Press
ISBN 13 : 1400831970
Total Pages : 321 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Outer Billiards on Kites by : Richard Evan Schwartz

Download or read book Outer Billiards on Kites written by Richard Evan Schwartz and published by Princeton University Press. This book was released on 2009-10-05 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system.