Combinatorial Algebraic Geometry

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Combinatorial Algebraic Geometry

Gregory G. Smith,Bernd Sturmfels
Combinatorial Algebraic Geometry Book PDF

Author : Gregory G. Smith,Bernd Sturmfels
Publisher : Springer
Page : 390 pages
File Size : 52,8 Mb
Release : 2017-11-17
Category : Mathematics
ISBN : 9781493974863

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Combinatorial Algebraic Geometry by Gregory G. Smith,Bernd Sturmfels Pdf

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.

Combinatorial Convexity and Algebraic Geometry

Günter Ewald
Combinatorial Convexity and Algebraic Geometry Book PDF

Author : Günter Ewald
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240440

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Combinatorial Convexity and Algebraic Geometry by Günter Ewald Pdf

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.

Combinatorial Algebraic Topology

Dimitry Kozlov
Combinatorial Algebraic Topology Book PDF

Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 43,7 Mb
Release : 2008-01-08
Category : Mathematics
ISBN : 3540730516

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Combinatorial Algebraic Topology by Dimitry Kozlov Pdf

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Combinatorial Algebraic Geometry

Aldo Conca,Sandra Di Rocco,Jan Draisma,June Huh,Bernd Sturmfels,Filippo Viviani
Combinatorial Algebraic Geometry Book PDF

Author : Aldo Conca,Sandra Di Rocco,Jan Draisma,June Huh,Bernd Sturmfels,Filippo Viviani
Publisher : Springer
Page : 239 pages
File Size : 42,6 Mb
Release : 2014-05-15
Category : Mathematics
ISBN : 9783319048703

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Combinatorial Algebraic Geometry by Aldo Conca,Sandra Di Rocco,Jan Draisma,June Huh,Bernd Sturmfels,Filippo Viviani Pdf

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications.

Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Combinatorial Aspects of Commutative Algebra and Algebraic Geometry Book PDF

Author : Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 45,7 Mb
Release : 2011-05-16
Category : Mathematics
ISBN : 9783642194924

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Combinatorial Aspects of Commutative Algebra and Algebraic Geometry by Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Knutsen Pdf

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.

Combinatorial Structures in Algebra and Geometry

Dumitru I. Stamate,Tomasz Szemberg
Combinatorial Structures in Algebra and Geometry Book PDF

Author : Dumitru I. Stamate,Tomasz Szemberg
Publisher : Springer Nature
Page : 182 pages
File Size : 52,8 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030521110

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Combinatorial Structures in Algebra and Geometry by Dumitru I. Stamate,Tomasz Szemberg Pdf

This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).

Combinatorial Commutative Algebra

Ezra Miller,Bernd Sturmfels
Combinatorial Commutative Algebra Book PDF

Author : Ezra Miller,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 46,7 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0387237070

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Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Pdf

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Connections Between Algebra, Combinatorics, and Geometry

Susan M. Cooper,Sean Sather-Wagstaff
Connections Between Algebra Combinatorics and Geometry Book PDF

Author : Susan M. Cooper,Sean Sather-Wagstaff
Publisher : Springer
Page : 317 pages
File Size : 54,8 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9781493906260

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Connections Between Algebra, Combinatorics, and Geometry by Susan M. Cooper,Sean Sather-Wagstaff Pdf

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Combinatorial Methods in Topology and Algebra

Bruno Benedetti,Emanuele Delucchi,Luca Moci
Combinatorial Methods in Topology and Algebra Book PDF

Author : Bruno Benedetti,Emanuele Delucchi,Luca Moci
Publisher : Springer
Page : 227 pages
File Size : 40,9 Mb
Release : 2015-10-31
Category : Mathematics
ISBN : 9783319201559

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Combinatorial Methods in Topology and Algebra by Bruno Benedetti,Emanuele Delucchi,Luca Moci Pdf

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.

Combinatorial Methods in Topology and Algebraic Geometry

John R. Harper,Richard Mandelbaum
Combinatorial Methods in Topology and Algebraic Geometry Book PDF

Author : John R. Harper,Richard Mandelbaum
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 47,5 Mb
Release : 1985
Category : Mathematics
ISBN : 0821850393

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Combinatorial Methods in Topology and Algebraic Geometry by John R. Harper,Richard Mandelbaum Pdf

A survey of the areas where combinatorial methods have proven especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces.

Combinatorial Geometry

János Pach,Pankaj K. Agarwal
Combinatorial Geometry Book PDF

Author : János Pach,Pankaj K. Agarwal
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 41,9 Mb
Release : 2011-10-18
Category : Mathematics
ISBN : 9781118031360

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Combinatorial Geometry by János Pach,Pankaj K. Agarwal Pdf

A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more

Combinatorial and Geometric Group Theory

Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Combinatorial and Geometric Group Theory Book PDF

Author : Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 51,7 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783764399115

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Combinatorial and Geometric Group Theory by Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura Pdf

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Combinatorics and Finite Geometry

Steven T. Dougherty
Combinatorics and Finite Geometry Book PDF

Author : Steven T. Dougherty
Publisher : Springer Nature
Page : 374 pages
File Size : 54,8 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030563950

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Combinatorics and Finite Geometry by Steven T. Dougherty Pdf

This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

New Perspectives in Algebraic Combinatorics

Louis J. Billera
New Perspectives in Algebraic Combinatorics Book PDF

Author : Louis J. Billera
Publisher : Cambridge University Press
Page : 360 pages
File Size : 40,6 Mb
Release : 1999-09-28
Category : Mathematics
ISBN : 0521770874

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New Perspectives in Algebraic Combinatorics by Louis J. Billera Pdf

This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.

Algebraic Combinatorics and Quantum Groups

Naihuan Jing
Algebraic Combinatorics and Quantum Groups Book PDF

Author : Naihuan Jing
Publisher : World Scientific
Page : 172 pages
File Size : 47,9 Mb
Release : 2003-06-27
Category : Science
ISBN : 9789814485500

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Algebraic Combinatorics and Quantum Groups by Naihuan Jing Pdf

Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics. This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields. Contents:Uno's Conjecture on Representation Types of Hecke Algebras (S Ariki)Quiver Varieties, Afine Lie Algebras, Algebras of BPS States, and Semicanonical Basis (I Frenkel et al.)Divided Differences of Type D and the Grassmannian of Complex Structures (H Duan & P Pragacz)Tableaux Statistics For Two Part Macdonald Polynomials (L Lapointe & J Morse)A Crystal to Rigged Configuration Bijection for Nonexceptional Affine Algebras (M Okado et al.)Littlewood's Formulas for Characters of Orthogonal and Symplectic Groups (A Lascoux)A q-Analog of Schur's Q-Functions (G Tudose & M Zabrocki) Readership: Researchers and graduate students in algebraic combinatorics, representation theory and quantum groups. Keywords:Algebras;Representation Theory;Polynomid;Varities;Q-Functions