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Interactions with Lattice Polytopes

2022-06-08 Mathematics
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Release : 2022-06-08
Genre : Mathematics
Kind : eBook
Book Rating : 277/5 ( reviews)

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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. This book was released on 2022-06-08. 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.

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

2019-05-30 Mathematics
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Release : 2019-05-30
Genre : Mathematics
Kind : eBook
Book Rating : 491/5 ( reviews)

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

Download or read book Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes written by Hibi Takayuki. This book was released on 2019-05-30. 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

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 603/5 ( reviews)

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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. This book was released on 2011. 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.

Lattice Polytopes in Geometry and Algebra

2014
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Release : 2014
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Book Synopsis Lattice Polytopes in Geometry and Algebra by : Andreas Paffenholz

Download or read book Lattice Polytopes in Geometry and Algebra written by Andreas Paffenholz. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt:

Interactions of Classical and Numerical Algebraic Geometry

2009-09-16 Mathematics
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Release : 2009-09-16
Genre : Mathematics
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Book Rating : 465/5 ( reviews)

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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. This book was released on 2009-09-16. 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.

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