Lectures On Random Lozenge Tilings

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Lectures On Random Lozenge Tilings

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Author : Vadim Gorin
language : en
Publisher: Cambridge University Press
Release Date : 2021-09-09

Lectures On Random Lozenge Tilings written by Vadim Gorin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Language Arts & Disciplines categories.

This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.

The Tiling Book

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Author : Colin Adams
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-28

The Tiling Book written by Colin Adams and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.

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

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Author : Yujiro Kawamata
language : en
Publisher: Cambridge University Press
Release Date : 2024-06-30

Algebraic Varieties Minimal Models And Finite Generation written by Yujiro Kawamata and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-30 with Mathematics categories.

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.

Homological Theory Of Representations

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Author : Henning Krause
language : en
Publisher: Cambridge University Press
Release Date : 2021-11-18

Homological Theory Of Representations written by Henning Krause and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Mathematics categories.

This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.

Elements Of Category Theory

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Author : Emily Riehl
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-10

Elements Of Category Theory written by Emily Riehl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.

This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.

Symmetry In Graphs

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Author : Ted Dobson
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-12

Symmetry In Graphs written by Ted Dobson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-12 with Language Arts & Disciplines categories.

The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

Dimension Groups And Dynamical Systems

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Author : Fabien Durand
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-03

Dimension Groups And Dynamical Systems written by Fabien Durand and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.

This is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.

The Geometry Of Cubic Hypersurfaces

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-29

The Geometry Of Cubic Hypersurfaces written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-29 with Mathematics categories.

A detailed introduction to cubic hypersurfaces, applying diverse techniques to a central class of algebraic varieties.

Equivariant Cohomology In Algebraic Geometry

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Author : David Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-26

Equivariant Cohomology In Algebraic Geometry written by David Anderson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-26 with Mathematics categories.

A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.

Optimal Mass Transport On Euclidean Spaces

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Author : Francesco Maggi
language : en
Publisher: Cambridge University Press
Release Date : 2023-11-16

Optimal Mass Transport On Euclidean Spaces written by Francesco Maggi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-16 with Mathematics categories.

A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.