Integer Points In Polyhedra Geometry Number Theory Representation Theory Algebra Optimization Statistics
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Integer Points in Polyhedra -- Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics by Matthias Beck Pdf
The AMS-IMS-SIAM Joint Summer Research Conference 'Integer Points in Polyhedra' was held in Snowbird, Utah in June 2006. This proceedings volume contains research and survey articles originating from the conference.
Integer Points in Polyhedra --- Geometry, Number Theory, Algebra, Optimization by Alexander Barvinok Pdf
The AMS-IMS-SIAM Summer Research Conference on Integer Points in Polyhedra took place in Snowbird (UT). This proceedings volume contains original research and survey articles stemming from that event. Topics covered include commutative algebra, optimization, discrete geometry, statistics, representation theory, and symplectic geometry. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.
Integer Points in Polyhedra by Alexander Barvinok Pdf
This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra-Lenstra-Lovasz lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.
Algebraic and Geometric Ideas in the Theory of Discrete Optimization by Jesus A. De Loera,Raymond Hemmecke,Matthias K?ppe Pdf
In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.
Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes by Hibi Takayuki,Tsuchiya Akiyoshi Pdf
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.
"Integers" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. Integers also houses a combinatorial games section. This work presents all papers of the 2013 volume in book form.
Computing the Continuous Discretely by Matthias Beck,Sinai Robins Pdf
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
Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf
This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held in Beijing, China, in September 2017. The 28 full papers presented in this volume were carefully reviewed and selected from 33 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.
Mirror Symmetry and Tropical Geometry by Ricardo Castaño-Bernard,Yan S. Soibelman,Ilia Zharkov Pdf
This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. --
Strings, Gauge Fields, and the Geometry Behind by Anton Rebhan,Ludmil Katzarkov,Johanna Knapp,Radoslav Rashkov,Emanuel Scheidegger Pdf
This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West. Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon. Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP. By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP. Contents:Gauge Field Theory, Anomalies, and Supersymmetry:BRST Symmetry and Cohomology (N Dragon and F Brandt)Aspects of Supersymmetric BRST Cohomology (F Brandt)Character Expansion for HOMFLY Polynomials: Integrability and Difference Equations (A Mironov, A Morozov and A Morozov)Bicategories in Field Theories — An Invitation (T Nikolaus and C Schweigert)The Compactification of IIB Supergravity on S5 Revisited (P van Nieuwenhuizen)String Theory and Algebraic Geometry:Max Kreuzer's Contributions to the Study of Calabi–Yau Manifolds (P Candelas)Calabi–Yau Three-Folds: Poincaré Polynomials and Fractals (A Ashmore and Y-H He)Conifold Degenerations of Fano 3-Folds as Hypersurfaces in Toric Varieties (V Batyrev and M Kreuzer)Nonassociativity in String Theory (R Blumenhagen)Counting Points and Hilbert Series in String Theory (V Braun)Standard Models and Calabi–Yaus (R Donagi)The String Landscape and Low Energy Supersymmetry (M R Douglas)The Cardy–Cartan Modular Invariant (J Fuchs, C Schweigert and C Stigner)A Projection to the Pure Spinor Space (S Guttenberg)Mathieu Moonshine and Symmetries of K3 Sigma Models (S Hohenegger)Toric Deligne–Mumford Stacks and the Better Behaved Version of the GKZ Hypergeometric System (R P Horja)Fano Polytopes (A M Kasprzyk and B Nill)Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT (J Polchinski and E Silverstein)Notes on the Relation Between Strings, Integrable Models and Gauge Theories (R C Rashkov)E11, Generalised Space-Time and IIA String Theory: The R ⊗ R Sector (A Rocén and P West)The Kreuzer Bi-Homomorphism (A N Schellekens)Emergent Spacetime and Black Hole Probes from Automorphic Forms (R Schimmrigk)How to Classify Reflexive Gorenstein Cones (H Skarke)PALP — A Package for Analyzing Lattice Polytopes:PALP — A User Manual (A P Braun, J Knapp, E Scheidegger, H Skarke and N-O Walliser) Readership: Graduate students and researchers in theoretical physics and mathematics. Keywords:String Theory;Gauge Theory;Algebraic Geometry;CalabiâYau Manifolds;Toric Geometry;Lattice Polytopes;BRST Symmetry;Cohomology;Anomalies;SupersymmetryKey Features:Original research articles contributed by prominent theoretical physicists and mathematicians (Victor Batyrev, Ralph Blumenhagen, Ron Donagi, Michael Douglas, Jürgen Fuchs, Alexei Morozov, Joseph Polchinski, Bert Schellekens, Christoph Schweigert, Eva Silverstein, Peter van Nieuwenhuizen, and Peter West, among others)Previously unpublished lecture notes on the classification of quantum gauge field anomalies by Friedemann Brandt and Norbert DragonA comprehensive manual and tutorial for the powerful software package PALP that was developed originally by Kreuzer and Skarke in connection with the classification of reflexive polytopes. Together with the publication of this memorial volume an overhauled version 2.1 of PALP will be released in the public domain
Maple in Mathematics Education and Research by Jürgen Gerhard,Ilias Kotsireas Pdf
This book constitutes the refereed proceedings of the third Maple Conference, MC 2019, held in Waterloo, Ontario, Canada, in October 2019. The 21 revised full papers and 9 short papers were carefully reviewed and selected out of 37 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.
Markov Bases in Algebraic Statistics by Satoshi Aoki,Hisayuki Hara,Akimichi Takemura Pdf
Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.
Algebraic and Geometric Ideas in the Theory of Discrete Optimization by Jesus A. De Loera,Raymond Hemmecke,Matthias K?ppe Pdf
This book presents recent advances in the mathematical theory of discrete optimization, particularly those supported by methods from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside the standard curriculum in optimization.
Geometry of Cuts and Metrics by Michel Marie Deza,Monique Laurent Pdf
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
