An Indefinite Excursion in Operator Theory
An Indefinite Excursion in Operator Theory

Author: Aurelian Gheondea

Publisher: Cambridge University Press

Published: 2022-07-28

Total Pages:

ISBN-13: 1108981275

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This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully highlights where difficulties arise and what tools are available to overcome them. With generous background material included in the appendices, this text is an excellent resource for researchers in operator theory, functional analysis, and related areas as well as for graduate students.

Modern Trends in Algebra and Representation Theory
Modern Trends in Algebra and Representation Theory

Author: David Jordan

Publisher: Cambridge University Press

Published: 2023-08-17

Total Pages: 407

ISBN-13: 1009097350

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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.

Elliptic Regularity Theory by Approximation Methods
Elliptic Regularity Theory by Approximation Methods

Author: Edgard A. Pimentel

Publisher: Cambridge University Press

Published: 2022-06-30

Total Pages: 204

ISBN-13: 1009103121

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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.

Maurer–Cartan Methods in Deformation Theory
Maurer–Cartan Methods in Deformation Theory

Author: Vladimir Dotsenko

Publisher: Cambridge University Press

Published: 2023-08-31

Total Pages: 187

ISBN-13: 1108965644

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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.

Stacks Project Expository Collection
Stacks Project Expository Collection

Author: Pieter Belmans

Publisher: Cambridge University Press

Published: 2022-09-30

Total Pages: 308

ISBN-13: 1009063286

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The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.

Surveys in Combinatorics 2022
Surveys in Combinatorics 2022

Author: Anthony Nixon

Publisher: Cambridge University Press

Published: 2022-06-09

Total Pages: 257

ISBN-13: 1009096222

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This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.

Bounded Cohomology and Simplicial Volume
Bounded Cohomology and Simplicial Volume

Author: Caterina Campagnolo

Publisher: Cambridge University Press

Published: 2022-11-17

Total Pages: 172

ISBN-13: 100919271X

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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.

Recent Developments in Algebraic Geometry
Recent Developments in Algebraic Geometry

Author: Hamid Abban

Publisher: Cambridge University Press

Published: 2022-09-30

Total Pages: 368

ISBN-13: 1009190822

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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.