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Effective Results And Methods For Diophantine Equations Over Finitely Generated Domains
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Book Synopsis Effective Results and Methods for Diophantine Equations over Finitely Generated Domains by : Jan-Hendrik Evertse
Download or read book Effective Results and Methods for Diophantine Equations over Finitely Generated Domains written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2022-04-28 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Number Theory, Analysis, and Combinatorics by : János Pintz
Download or read book Number Theory, Analysis, and Combinatorics written by János Pintz and published by Walter de Gruyter. This book was released on 2013-12-12 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Turán, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the János Bolyai Mathematical Society and the Mathematical Institute of Eötvös Loránd University organized an international conference devoted to Paul Turán's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics. The conference was held in Budapest, August 22-26, 2011. Some of the invited lectures reviewed different aspects of Paul Turán's work and influence. Most of the lectures allowed participants to report about their own work in the above mentioned areas of mathematics.
Book Synopsis Unit Equations in Diophantine Number Theory by : Jan-Hendrik Evertse
Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.
Book Synopsis Discrete Quantum Walks on Graphs and Digraphs by : Chris Godsil
Download or read book Discrete Quantum Walks on Graphs and Digraphs written by Chris Godsil and published by Cambridge University Press. This book was released on 2022-12-31 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Download or read book Rectifiability written by Pertti Mattila and published by Cambridge University Press. This book was released on 2023-01-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside.
Book Synopsis Elliptic Regularity Theory by Approximation Methods by : Edgard A. Pimentel
Download or read book Elliptic Regularity Theory by Approximation Methods written by Edgard A. Pimentel and published by Cambridge University Press. This book was released on 2022-06-30 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs – such as the Krylov–Safonov and Evans–Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ – and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and Hölder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hölder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.
Book Synopsis Maurer–Cartan Methods in Deformation Theory by : Vladimir Dotsenko
Download or read book Maurer–Cartan Methods in Deformation Theory written by Vladimir Dotsenko and published by Cambridge University Press. This book was released on 2023-08-31 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Developments in Algebraic Geometry by : Hamid Abban
Download or read book Recent Developments in Algebraic Geometry written by Hamid Abban and published by Cambridge University Press. This book was released on 2022-09-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field – this book hopes to inspire a new generation of graduate students and researchers in his tradition.
Book Synopsis Bounded Cohomology and Simplicial Volume by : Caterina Campagnolo
Download or read book Bounded Cohomology and Simplicial Volume written by Caterina Campagnolo and published by Cambridge University Press. This book was released on 2022-11-17 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their introduction by Gromov in the 1980s, the study of bounded cohomology and simplicial volume has developed into an active field connected to geometry and group theory. This monograph, arising from a learning seminar for young researchers working in the area, provides a collection of different perspectives on the subject, both classical and recent. The book's introduction presents the main definitions of the theories of bounded cohomology and simplicial volume, outlines their history, and explains their principal motivations and applications. Individual chapters then present different aspects of the theory, with a focus on examples. Detailed references to foundational papers and the latest research are given for readers wishing to dig deeper. The prerequisites are only basic knowledge of classical algebraic topology and of group theory, and the presentations are gentle and informal in order to be accessible to beginning graduate students wanting to enter this lively and topical field.
Book Synopsis Surveys in Combinatorics 2022 by : Anthony Nixon
Download or read book Surveys in Combinatorics 2022 written by Anthony Nixon and published by Cambridge University Press. This book was released on 2022-06-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Book Synopsis Modern Trends in Algebra and Representation Theory by : David Jordan
Download or read book Modern Trends in Algebra and Representation Theory written by David Jordan and published by Cambridge University Press. This book was released on 2023-08-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
Book Synopsis The Logical Approach to Automatic Sequences by : Jeffrey Shallit
Download or read book The Logical Approach to Automatic Sequences written by Jeffrey Shallit and published by Cambridge University Press. This book was released on 2022-09-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Calabi Problem for Fano Threefolds by : Carolina Araujo
Download or read book The Calabi Problem for Fano Threefolds written by Carolina Araujo and published by Cambridge University Press. This book was released on 2023-06-30 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Combinatorics and the Monster Group by : Alexander A. Ivanov
Download or read book Algebraic Combinatorics and the Monster Group written by Alexander A. Ivanov and published by Cambridge University Press. This book was released on 2023-08-17 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering, 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.
Book Synopsis Surveys in Combinatorics 2024 by : Felix Fischer
Download or read book Surveys in Combinatorics 2024 written by Felix Fischer and published by Cambridge University Press. This book was released on 2024-06-13 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Book Synopsis C∞-Algebraic Geometry with Corners by : Kelli Francis-Staite
Download or read book C∞-Algebraic Geometry with Corners written by Kelli Francis-Staite and published by Cambridge University Press. This book was released on 2023-12-31 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schemes 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.
Book Synopsis Facets of Algebraic Geometry by : Paolo Aluffi
Download or read book Facets of Algebraic Geometry written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2022-04-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
