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Author: Konrad K. Dabrowski
Publisher: Cambridge University Press
Published: 2021-06-24
Total Pages: 379
ISBN-13: 1009018884
DOWNLOAD EBOOKThese nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.
Author: Felix Fischer
Publisher: Cambridge University Press
Published: 2024-06-13
Total Pages: 305
ISBN-13: 1009490532
DOWNLOAD EBOOKThis volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Author: Anthony Nixon
Publisher: Cambridge University Press
Published: 2022-06-09
Total Pages: 257
ISBN-13: 1009096222
DOWNLOAD EBOOKThis volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Author: R. A. Bailey
Publisher: Cambridge University Press
Published: 2024-05-30
Total Pages: 452
ISBN-13: 1009465945
DOWNLOAD EBOOKThis collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Author: Kelli Francis-Staite
Publisher: Cambridge University Press
Published: 2023-12-31
Total Pages: 224
ISBN-13: 1009400207
DOWNLOAD EBOOKSchemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
Author: Chris Godsil
Publisher: Cambridge University Press
Published: 2022-12-31
Total Pages: 151
ISBN-13: 1009261681
DOWNLOAD EBOOKExplore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Author: Alexander A. Ivanov
Publisher: Cambridge University Press
Published: 2023-08-17
Total Pages: 584
ISBN-13: 1009338056
DOWNLOAD EBOOKCovering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Author: Uwe Nagel
Publisher: Springer Nature
Published: 2024
Total Pages: 234
ISBN-13: 9819738865
DOWNLOAD EBOOKThe study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds. Recent developments have demonstrated important cases of the Lefschetz property beyond the original geometric settings, such as Coxeter groups or matroids. Furthermore, there are connections to other branches of mathematics, for example, commutative algebra, algebraic topology, and combinatorics. Important results in this area have been obtained by finding unexpected connections between apparently different topics. A conference in Cortona, Italy in September 2022 brought together researchers discussing recent developments and working on new problems related to the Lefschetz properties. The book will feature surveys on several aspects of the theory as well as articles on new results and open problems.
Author: Jeffrey Shallit
Publisher: Cambridge University Press
Published: 2022-09-30
Total Pages: 376
ISBN-13: 1108786979
DOWNLOAD EBOOKAutomatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Author: Carolina Araujo
Publisher: Cambridge University Press
Published: 2023-06-30
Total Pages: 452
ISBN-13: 1009239651
DOWNLOAD EBOOKAlgebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kähler–Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kähler–Einstein metric, containing many additional relevant results such as the classification of all Kähler–Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.
