Lectures on Random Lozenge Tilings PDF Download
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Author: Vadim Gorin
Publisher: Cambridge University Press
ISBN: 1108843964
Category : Language Arts & Disciplines
Languages : en
Pages : 261
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Book Description
This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
Author: Vadim Gorin
Publisher: Cambridge University Press
ISBN: 1108843964
Category : Language Arts & Disciplines
Languages : en
Pages : 261
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Book Description
This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
Author: Colin Adams
Publisher: American Mathematical Society
ISBN: 1470474611
Category : Mathematics
Languages : en
Pages : 310
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Book Description
Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.
Author: Yujiro Kawamata
Publisher: Cambridge University Press
ISBN: 1009344676
Category : Mathematics
Languages : en
Pages : 263
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Book Description
The finite generation theorem is a major achievement of modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic zero is a finitely generated graded ring. This graduate-level text is the first to explain this proof. It covers the progress on the minimal model theory over the last 30 years, culminating in the landmark paper on finite generation by Birkar-Cascini-Hacon-McKernan. Building up to this proof, the author presents important results and techniques that are now part of the standard toolbox of birational geometry, including Mori's bend and break method, vanishing theorems, positivity theorems and Siu's analysis on multiplier ideal sheaves. Assuming only the basics in algebraic geometry, the text keeps prerequisites to a minimum with self-contained explanations of terminology and theorems.
Author: Ted Dobson
Publisher: Cambridge University Press
ISBN: 1108429068
Category : Language Arts & Disciplines
Languages : en
Pages : 527
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Book Description
The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.
Author: Henning Krause
Publisher: Cambridge University Press
ISBN: 1108838898
Category : Mathematics
Languages : en
Pages : 517
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Book Description
This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.
Author: Emily Riehl
Publisher: Cambridge University Press
ISBN: 1108837980
Category : Mathematics
Languages : en
Pages : 781
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Book Description
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
Author: Fabien Durand
Publisher: Cambridge University Press
ISBN: 1108986099
Category : Mathematics
Languages : en
Pages : 594
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Book Description
This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.
Author: Francesco Maggi
Publisher: Cambridge University Press
ISBN: 1009179705
Category : Mathematics
Languages : en
Pages : 317
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Book Description
A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.
Author: David Anderson
Publisher: Cambridge University Press
ISBN: 1009349988
Category : Mathematics
Languages : en
Pages : 463
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Book Description
A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.
Author: Daniel Huybrechts
Publisher: Cambridge University Press
ISBN: 1009280007
Category : Mathematics
Languages : en
Pages : 461
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Book Description
A detailed introduction to cubic hypersurfaces, applying diverse techniques to a central class of algebraic varieties.
