Lectures on Random Lozenge Tilings
Title | Lectures on Random Lozenge Tilings PDF eBook |
Author | Vadim Gorin |
Publisher | Cambridge University Press |
Pages | 261 |
Release | 2021-09-09 |
Genre | Language Arts & Disciplines |
ISBN | 1108843964 |
This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
The Tiling Book
Title | The Tiling Book PDF eBook |
Author | Colin Adams |
Publisher | American Mathematical Society |
Pages | 310 |
Release | 2023-08-28 |
Genre | Mathematics |
ISBN | 1470474611 |
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.
Algebraic Varieties: Minimal Models and Finite Generation
Title | Algebraic Varieties: Minimal Models and Finite Generation PDF eBook |
Author | Yujiro Kawamata |
Publisher | Cambridge University Press |
Pages | 263 |
Release | 2024-06-30 |
Genre | Mathematics |
ISBN | 1009344676 |
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.
Symmetry in Graphs
Title | Symmetry in Graphs PDF eBook |
Author | Ted Dobson |
Publisher | Cambridge University Press |
Pages | 527 |
Release | 2022-05-12 |
Genre | Language Arts & Disciplines |
ISBN | 1108429068 |
The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.
Homological Theory of Representations
Title | Homological Theory of Representations PDF eBook |
Author | Henning Krause |
Publisher | Cambridge University Press |
Pages | 517 |
Release | 2021-11-18 |
Genre | Mathematics |
ISBN | 1108838898 |
This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.
Elements of ?-Category Theory
Title | Elements of ?-Category Theory PDF eBook |
Author | Emily Riehl |
Publisher | Cambridge University Press |
Pages | 781 |
Release | 2022-02-10 |
Genre | Mathematics |
ISBN | 1108837980 |
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
Dimension Groups and Dynamical Systems
Title | Dimension Groups and Dynamical Systems PDF eBook |
Author | Fabien Durand |
Publisher | Cambridge University Press |
Pages | 594 |
Release | 2022-02-03 |
Genre | Mathematics |
ISBN | 1108986099 |
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.