Fourier Restriction, Decoupling, and Applications

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Publisher : Cambridge University Press
ISBN 13 : 1108603610
Total Pages : 349 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Fourier Restriction, Decoupling, and Applications by : Ciprian Demeter

Download or read book Fourier Restriction, Decoupling, and Applications written by Ciprian Demeter and published by Cambridge University Press. This book was released on 2020-01-02 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain–Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.

Recent Developments in Harmonic Analysis and its Applications

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Publisher : American Mathematical Society
ISBN 13 : 147047140X
Total Pages : 182 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Developments in Harmonic Analysis and its Applications by : Shaoming Guo

Download or read book Recent Developments in Harmonic Analysis and its Applications written by Shaoming Guo and published by American Mathematical Society. This book was released on 2024-01-24 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Harmonic Analysis, held from March 26–27, 2022. Harmonic analysis has gone through rapid developments in the past decade. New tools, including multilinear Kakeya inequalities, broad-narrow analysis, polynomial methods, decoupling inequalities, and refined Strichartz inequalities, are playing a crucial role in resolving problems that were previously considered out of reach. A large number of important works in connection with geometric measure theory, analytic number theory, partial differential equations, several complex variables, etc., have appeared in the last few years. This book collects some examples of this work.

Polynomial Methods and Incidence Theory

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Publisher : Cambridge University Press
ISBN 13 : 1108963013
Total Pages : 264 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Polynomial Methods and Incidence Theory by : Adam Sheffer

Download or read book Polynomial Methods and Incidence Theory written by Adam Sheffer and published by Cambridge University Press. This book was released on 2022-03-24 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.

Toeplitz Matrices and Operators

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Publisher : Cambridge University Press
ISBN 13 : 110719850X
Total Pages : 453 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Toeplitz Matrices and Operators by : Nikolaï Nikolski

Download or read book Toeplitz Matrices and Operators written by Nikolaï Nikolski and published by Cambridge University Press. This book was released on 2020-01-02 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.

Foundations of Stable Homotopy Theory

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Publisher : Cambridge University Press
ISBN 13 : 1108672671
Total Pages : 432 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Foundations of Stable Homotopy Theory by : David Barnes

Download or read book Foundations of Stable Homotopy Theory written by David Barnes and published by Cambridge University Press. This book was released on 2020-03-26 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.

The Character Theory of Finite Groups of Lie Type

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Publisher : Cambridge University Press
ISBN 13 : 1108808905
Total Pages : 406 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis The Character Theory of Finite Groups of Lie Type by : Meinolf Geck

Download or read book The Character Theory of Finite Groups of Lie Type written by Meinolf Geck and published by Cambridge University Press. This book was released on 2020-02-27 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.

Higher Index Theory

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Publisher : Cambridge University Press
ISBN 13 : 1108491065
Total Pages : 595 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Higher Index Theory by : Rufus Willett

Download or read book Higher Index Theory written by Rufus Willett and published by Cambridge University Press. This book was released on 2020-07-02 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.

Generators of Markov Chains

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Publisher : Cambridge University Press
ISBN 13 : 1108495796
Total Pages : 279 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Generators of Markov Chains by : Adam Bobrowski

Download or read book Generators of Markov Chains written by Adam Bobrowski and published by Cambridge University Press. This book was released on 2020-11-26 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.

Derived Categories

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Publisher : Cambridge University Press
ISBN 13 : 1108321607
Total Pages : 622 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Derived Categories by : Amnon Yekutieli

Download or read book Derived Categories written by Amnon Yekutieli and published by Cambridge University Press. This book was released on 2019-12-19 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra. It carefully explains the foundations in detail before moving on to key applications in commutative and noncommutative algebra, many otherwise unavailable outside of research articles. These include commutative and noncommutative dualizing complexes, perfect DG modules, and tilting DG bimodules. Written with graduate students in mind, the emphasis here is on explicit constructions (with many examples and exercises) as opposed to axiomatics, with the goal of demystifying this difficult subject. Beyond serving as a thorough introduction for students, it will serve as an important reference for researchers in algebra, geometry and mathematical physics.

From Categories to Homotopy Theory

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Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis From Categories to Homotopy Theory by : Birgit Richter

Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

Optimal Mass Transport on Euclidean Spaces

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Publisher : Cambridge University Press
ISBN 13 : 1009179705
Total Pages : 317 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Optimal Mass Transport on Euclidean Spaces by : Francesco Maggi

Download or read book Optimal Mass Transport on Euclidean Spaces written by Francesco Maggi and published by Cambridge University Press. This book was released on 2023-10-31 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.

Equivariant Cohomology in Algebraic Geometry

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Publisher : Cambridge University Press
ISBN 13 : 1009349988
Total Pages : 463 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Equivariant Cohomology in Algebraic Geometry by : David Anderson

Download or read book Equivariant Cohomology in Algebraic Geometry written by David Anderson and published by Cambridge University Press. This book was released on 2023-11-30 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.

The Geometry of Cubic Hypersurfaces

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Publisher : Cambridge University Press
ISBN 13 : 1009280007
Total Pages : 461 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis The Geometry of Cubic Hypersurfaces by : Daniel Huybrechts

Download or read book The Geometry of Cubic Hypersurfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2023-06-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed introduction to cubic hypersurfaces, applying diverse techniques to a central class of algebraic varieties.

Symmetry in Graphs

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Publisher : Cambridge University Press
ISBN 13 : 1108429068
Total Pages : 527 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Symmetry in Graphs by : Ted Dobson

Download or read book Symmetry in Graphs written by Ted Dobson and published by Cambridge University Press. This book was released on 2022-05-12 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

Harmonic Functions and Random Walks on Groups

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Publisher : Cambridge University Press
ISBN 13 : 1009546570
Total Pages : 404 pages
Book Rating : 4.0/5 (95 download)

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Book Synopsis Harmonic Functions and Random Walks on Groups by : Ariel Yadin

Download or read book Harmonic Functions and Random Walks on Groups written by Ariel Yadin and published by Cambridge University Press. This book was released on 2024-05-31 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet–Deny Theorem, the Milnor–Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.

Geometric Inverse Problems

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Publisher : Cambridge University Press
ISBN 13 : 1009041428
Total Pages : 370 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Geometric Inverse Problems by : Gabriel P. Paternain

Download or read book Geometric Inverse Problems written by Gabriel P. Paternain and published by Cambridge University Press. This book was released on 2023-01-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.

Homological Methods in Banach Space Theory

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Publisher : Cambridge University Press
ISBN 13 : 1108807887
Total Pages : 562 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Homological Methods in Banach Space Theory by : Félix Cabello Sánchez

Download or read book Homological Methods in Banach Space Theory written by Félix Cabello Sánchez and published by Cambridge University Press. This book was released on 2023-01-31 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.