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| Author | : Masaki Kashiwara |
| Publisher | : Cambridge University Press |
| Total Pages | : 119 |
| Release | : 2016-05-26 |
| Genre | : Mathematics |
| ISBN | : 1316613453 |
A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.
| Author | : Masaki Kashiwara |
| Publisher | : |
| Total Pages | : 111 |
| Release | : 2016 |
| Genre | : D-modules |
| ISBN | : 9781316675625 |
| Author | : Scott Balchin |
| Publisher | : Cambridge University Press |
| Total Pages | : 357 |
| Release | : 2021-11-18 |
| Genre | : Mathematics |
| ISBN | : 1108931944 |
A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.
| Author | : Pieter Belmans |
| Publisher | : Cambridge University Press |
| Total Pages | : 307 |
| Release | : 2022-10-31 |
| Genre | : Mathematics |
| ISBN | : 1009054856 |
A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.
| Author | : Jan-Hendrik Evertse |
| Publisher | : Cambridge University Press |
| Total Pages | : 242 |
| Release | : 2022-04-28 |
| Genre | : Mathematics |
| ISBN | : 1009050036 |
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
| Author | : Paolo Aluffi |
| Publisher | : Cambridge University Press |
| Total Pages | : 395 |
| Release | : 2022-04-07 |
| Genre | : Mathematics |
| ISBN | : 1108792510 |
Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
| Author | : Jeffrey Shallit |
| Publisher | : Cambridge University Press |
| Total Pages | : 376 |
| Release | : 2022-09-30 |
| Genre | : Computers |
| ISBN | : 1108786979 |
Automatic 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 | : Vladimir Dotsenko |
| Publisher | : Cambridge University Press |
| Total Pages | : 188 |
| Release | : 2023-08-31 |
| Genre | : Mathematics |
| ISBN | : 1108967027 |
Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
| Author | : Anthony Nixon |
| Publisher | : Cambridge University Press |
| Total Pages | : 258 |
| Release | : 2022-06-09 |
| Genre | : Mathematics |
| ISBN | : 1009115464 |
This volume contains eight survey articles by the invited speakers of the 29th British Combinatorial Conference, held at Lancaster University in July 2022. Each article provides an overview of recent developments in a current hot research topic in combinatorics. These topics span graphs and hypergraphs, Latin squares, linear programming, finite fields, extremal combinatorics, Ramsey theory, graph minors and tropical geometry. The authors are among the world's foremost researchers on their respective topics but their surveys are aimed at nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, making the latest developments accessible to researchers and graduate students in mathematics and theoretical computer science with an interest in combinatorics and helping them to keep abreast of the field.
| Author | : Carolina Araujo |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 2023-06-30 |
| Genre | : Mathematics |
| ISBN | : 1009239651 |
Algebraic 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.
