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Combinatorial Convexity And Algebraic Geometry
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Book Synopsis Combinatorial Convexity and Algebraic Geometry by : Günter Ewald
Download or read book Combinatorial Convexity and Algebraic Geometry written by Günter Ewald and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorial Convexity and Algebraic Geometry by : G. Ewald
Download or read book Combinatorial Convexity and Algebraic Geometry written by G. Ewald and published by . This book was released on 1997 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Convexity by : Imre Bárány
Download or read book Combinatorial Convexity written by Imre Bárány and published by American Mathematical Soc.. This book was released on 2021-11-04 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
Book Synopsis Combinatorial Algebraic Geometry by : Gregory G. Smith
Download or read book Combinatorial Algebraic Geometry written by Gregory G. Smith and published by Springer. This book was released on 2017-11-17 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.
Book Synopsis Handbook of Convex Geometry by : Gerard Meurant
Download or read book Handbook of Convex Geometry written by Gerard Meurant and published by Elsevier. This book was released on 2014-06-28 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.
Book Synopsis Convexity and Related Combinatorial Geometry by : David C. Kay
Download or read book Convexity and Related Combinatorial Geometry written by David C. Kay and published by . This book was released on 1982 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Vladimir Boltyanski Publisher :Springer Science & Business Media ISBN 13 :9783540613411 Total Pages :446 pages Book Rating :4.6/5 (134 download)
Book Synopsis Excursions into Combinatorial Geometry by : Vladimir Boltyanski
Download or read book Excursions into Combinatorial Geometry written by Vladimir Boltyanski and published by Springer Science & Business Media. This book was released on 1996-11-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the combinatorial geometry of convex bodies in finite-dimensional spaces. A general introduction to geometric convexity is followed by the investigation of d-convexity and H-convexity, and by various applications. Recent research is discussed, for example the three problems from the combinatorial geometry of convex bodies (unsolved in the general case): the Szoekefalvi-Nagy problem, the Borsuk problem, the Hadwiger covering problem. These and related questions are then applied to a new class of convex bodies which is a natural generalization of the class of zonoids: the class of belt bodies. Finally open research problems are discussed. Each section is supplemented by a wide range of exercises and the geometric approach to many topics is illustrated with the help of more than 250 figures.
Book Synopsis Algebraic and Geometric Combinatorics by : Christos A. Athanasiadis
Download or read book Algebraic and Geometric Combinatorics written by Christos A. Athanasiadis and published by American Mathematical Soc.. This book was released on 2006 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Book Synopsis Foundations of Convex Geometry by : W. A. Coppel
Download or read book Foundations of Convex Geometry written by W. A. Coppel and published by Cambridge University Press. This book was released on 1998-03-05 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained and thorough book on the foundations of Euclidean geometry.
Book Synopsis Combinatorial and Computational Geometry by : Jacob E. Goodman
Download or read book Combinatorial and Computational Geometry written by Jacob E. Goodman and published by Cambridge University Press. This book was released on 2005-08-08 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Book Synopsis Selected Topics in Convex Geometry by : Maria Moszynska
Download or read book Selected Topics in Convex Geometry written by Maria Moszynska and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines in detail those topics in convex geometry that are concerned with Euclidean space Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization
Book Synopsis Discrete and Computational Geometry by : Boris Aronov
Download or read book Discrete and Computational Geometry written by Boris Aronov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 853 pages. Available in PDF, EPUB and Kindle. Book excerpt: An impressive collection of original research papers in discrete and computational geometry, contributed by many leading researchers in these fields, as a tribute to Jacob E. Goodman and Richard Pollack, two of the ‘founding fathers’ of the area, on the occasion of their 2/3 x 100 birthdays. The topics covered by the 41 papers provide professionals and graduate students with a comprehensive presentation of the state of the art in most aspects of discrete and computational geometry, including geometric algorithms, study of arrangements, geometric graph theory, quantitative and algorithmic real algebraic geometry, with important connections to algebraic geometry, convexity, polyhedral combinatorics, the theory of packing, covering, and tiling. The book serves as an invaluable source of reference in this discipline.
Book Synopsis Convexity and Its Applications by : GRUBER
Download or read book Convexity and Its Applications written by GRUBER and published by Birkhäuser. This book was released on 2013-11-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.
Book Synopsis Combinatorial Aspects of Commutative Algebra and Algebraic Geometry by : Gunnar Fløystad
Download or read book Combinatorial Aspects of Commutative Algebra and Algebraic Geometry written by Gunnar Fløystad and published by Springer Science & Business Media. This book was released on 2011-05-16 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.
Book Synopsis Combinatorial Geometry in the Plane by : Hugo Hadwiger
Download or read book Combinatorial Geometry in the Plane written by Hugo Hadwiger and published by Courier Corporation. This book was released on 2015-01-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate-level text discusses theorems on topics restricted to the plane, such as convexity, coverings, and graphs. Two-part treatment begins with specific topics followed by an extensive selection of short proofs. 1964 edition.
Book Synopsis Geometric Algorithms and Combinatorial Optimization by : Martin Grötschel
Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.
