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

Author: Takayuki Hibi

Publisher: World Scientific

Published: 2019-05-30

Total Pages: 476

ISBN-13: 9811200491

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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
Algebraic and Geometric Combinatorics on Lattice Polytopes

Author: Takayuki Hibi

Publisher: World Scientific Publishing Company

Published: 2019

Total Pages: 0

ISBN-13: 9789811200472

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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 Statistics for Computational Biology
Algebraic Statistics for Computational Biology

Author: L. Pachter

Publisher: Cambridge University Press

Published: 2005-08-22

Total Pages: 440

ISBN-13: 9780521857000

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This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

Computational Algebraic Geometry
Computational Algebraic Geometry

Author: Frederic Eyssette

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 334

ISBN-13: 1461227526

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The theory and practice of computation in algebraic geometry and related domains, from a mathematical point of view, has generated an increasing interest both for its rich theoretical possibilities and its usefulness in applications in science and engineering. In fact, it is one of the master keys for future significant improvement of the computer algebra systems (e.g., Reduce, Macsyma, Maple, Mathematica, Axiom, Macaulay, etc.) that have become such useful tools for many scientists in a variety of disciplines. The major themes covered in this volume, arising from papers p- sented at the conference MEGA-92 were: - Effective methods and complexity issues in commutative algebra, projective geometry, real geometry, and algebraic number theory - Algebra-geometric methods in algebraic computing and applica tions. MEGA-92 was the second of a new series of European conferences on the general theme of Effective Methods in Algebraic Geometry. It was held in Nice, France, on April 21-25, 1992 and built on the themes presented at MEGA-90 (Livomo, Italy, April 17-21, 1990). The next conference - MEGA-94 - will be held in Santander, Spain in the spring of 1994. The Organizing committee that initiatiod and supervises this bi enniel conference consists of A. Conte (Torino), J.H. Davenport (Bath), A. Galligo (Nice), D. Yu. Grigoriev (Petersburg), J. Heintz (Buenos Aires), W. Lassner (Leipzig), D. Lazard (paris), H.M. MOller (Hagen), T. Mora (Genova), M. Pohst (DUsseldort), T. Recio (Santander), J.J.

Existence of Unimodular Triangulations–Positive Results
Existence of Unimodular Triangulations–Positive Results

Author: Christian Haase

Publisher: American Mathematical Soc.

Published: 2021-07-21

Total Pages: 83

ISBN-13: 1470447169

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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.

Algebra, Geometry and Software Systems
Algebra, Geometry and Software Systems

Author: Michael Joswig

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 332

ISBN-13: 3662051486

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A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

A Celebration of Algebraic Geometry
A Celebration of Algebraic Geometry

Author: Brendan Hassett

Publisher: American Mathematical Soc.

Published: 2013-09-11

Total Pages: 614

ISBN-13: 0821889834

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This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Combinatorial Reciprocity Theorems
Combinatorial Reciprocity Theorems

Author: Matthias Beck

Publisher: American Mathematical Soc.

Published: 2018-12-12

Total Pages: 325

ISBN-13: 147042200X

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Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.

Combinatorial Structures in Algebra and Geometry
Combinatorial Structures in Algebra and Geometry

Author: Dumitru I. Stamate

Publisher: Springer Nature

Published: 2020-09-01

Total Pages: 182

ISBN-13: 3030521117

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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).