Iwasawa Theory and Its Perspective, Volume 1

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Publisher : American Mathematical Society
ISBN 13 : 1470456729
Total Pages : 167 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 1 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 1 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2023-05-03 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory. The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects. The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.

Iwasawa Theory and Its Perspective, Volume 2

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Publisher : American Mathematical Society
ISBN 13 : 1470456737
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 2 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.

Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory

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Publisher : American Mathematical Society
ISBN 13 : 1470478099
Total Pages : 555 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory by : Donald Yau

Download or read book Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory written by Donald Yau and published by American Mathematical Society. This book was released on 2024-10-08 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. The three books published by the AMS in the Mathematical Surveys and Monographs series under the general title Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories?this book, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra) provide a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic $K$-theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user-friendly resource for beginners and experts alike. Part 1 of this book proves in detail Laplaza's two coherence theorems and May's strictification theorem of symmetric bimonoidal categories, as well as their bimonoidal analogues. This part includes detailed corrections to several inaccurate statements and proofs found in the literature. Part 2 proves Baez's Conjecture on the existence of a bi-initial object in a 2-category of symmetric bimonoidal categories. The next main theorem states that a matrix construction, involving the matrix product and the matrix tensor product, sends a symmetric bimonoidal category with invertible distributivity morphisms to a symmetric monoidal bicategory, with no strict structure morphisms in general.

Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory

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Publisher : American Mathematical Society
ISBN 13 : 1470478110
Total Pages : 633 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory by : Niles Johnson

Download or read book Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory written by Niles Johnson and published by American Mathematical Society. This book was released on 2024-10-23 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. The three books published by the AMS in the Mathematical Surveys and Monographs series under the title Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra?this book) provide a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic $K$-theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user-friendly resource for beginners and experts alike. Part 1 of this book is a detailed study of enriched monoidal categories, pointed diagram categories, and enriched multicategories. Using this machinery, Part 2 discusses the rich interconnection between the higher ring-like categories, homotopy theory, and algebraic $K$-theory. Starting with a chapter on homotopy theory background, the first half of Part 2 constructs the Segal $K$-theory functor and the Elmendorf-Mandell $K$-theory multifunctor from permutative categories to symmetric spectra. For the latter, the detailed treatment here includes identification and correction of some subtle errors concerning its extended domain. The second half applies the $K$-theory multifunctor to small ring, bipermutative, braided ring, and $E_n$-monoidal categories to obtain, respectively, strict ring, $E_{infty}$-, $E_2$-, and $E_n$-symmetric spectra.

Trees of Hyperbolic Spaces

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Publisher : American Mathematical Society
ISBN 13 : 1470474255
Total Pages : 295 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Trees of Hyperbolic Spaces by : Michael Kapovich

Download or read book Trees of Hyperbolic Spaces written by Michael Kapovich and published by American Mathematical Society. This book was released on 2024-08-15 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an alternative proof of the Bestvina?Feighn combination theorem for trees of hyperbolic spaces and describes uniform quasigeodesics in such spaces. As one of the applications of their description of uniform quasigeodesics, the authors prove the existence of Cannon?Thurston maps for inclusion maps of total spaces of subtrees of hyperbolic spaces and of relatively hyperbolic spaces. They also analyze the structure of Cannon?Thurston laminations in this setting. Furthermore, some group-theoretic applications of these results are discussed. This book also contains background material on coarse geometry and geometric group theory.

The Classification of the Finite Simple Groups, Number 10

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Publisher : American Mathematical Society
ISBN 13 : 1470475537
Total Pages : 587 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Classification of the Finite Simple Groups, Number 10 by : Inna Capdeboscq

Download or read book The Classification of the Finite Simple Groups, Number 10 written by Inna Capdeboscq and published by American Mathematical Society. This book was released on 2023-10-23 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.

Applications of Group Theory in Cryptography

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Publisher : American Mathematical Society
ISBN 13 : 1470474697
Total Pages : 162 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Applications of Group Theory in Cryptography by : Delaram Kahrobaei

Download or read book Applications of Group Theory in Cryptography written by Delaram Kahrobaei and published by American Mathematical Society. This book was released on 2024-03-25 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography. The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography. The book is a monograph addressed to graduate students and researchers in both mathematics and computer science.

Recovery Methodologies: Regularization and Sampling

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Publisher : American Mathematical Society
ISBN 13 : 1470473453
Total Pages : 505 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recovery Methodologies: Regularization and Sampling by : Willi Freeden

Download or read book Recovery Methodologies: Regularization and Sampling written by Willi Freeden and published by American Mathematical Society. This book was released on 2023-08-21 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.

Residuated Structures in Algebra and Logic

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Publisher : American Mathematical Society
ISBN 13 : 1470469855
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Residuated Structures in Algebra and Logic by : George Metcalfe

Download or read book Residuated Structures in Algebra and Logic written by George Metcalfe and published by American Mathematical Society. This book was released on 2023-11-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.

Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators

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Publisher : American Mathematical Society
ISBN 13 : 1470474654
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators by : Horst R. Thieme

Download or read book Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators written by Horst R. Thieme and published by American Mathematical Society. This book was released on 2024-05-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

Self-similar and Self-affine Sets and Measures

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Publisher : American Mathematical Society
ISBN 13 : 1470470462
Total Pages : 466 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Self-similar and Self-affine Sets and Measures by : Balázs Bárány

Download or read book Self-similar and Self-affine Sets and Measures written by Balázs Bárány and published by American Mathematical Society. This book was released on 2023-11-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.

Automorphic Forms Beyond $mathrm {GL}_2$

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Publisher : American Mathematical Society
ISBN 13 : 1470474921
Total Pages : 199 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Automorphic Forms Beyond $mathrm {GL}_2$ by : Ellen Elizabeth Eischen

Download or read book Automorphic Forms Beyond $mathrm {GL}_2$ written by Ellen Elizabeth Eischen and published by American Mathematical Society. This book was released on 2024-03-26 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Elementary Modular Iwasawa Theory

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Publisher : World Scientific
ISBN 13 : 9811241384
Total Pages : 446 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Elementary Modular Iwasawa Theory by : Haruzo Hida

Download or read book Elementary Modular Iwasawa Theory written by Haruzo Hida and published by World Scientific. This book was released on 2021-10-04 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows:Many open problems are presented to stimulate young researchers pursuing their field of study.

Number Theory 1

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821808634
Total Pages : 180 pages
Book Rating : 4.8/5 (86 download)

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Book Synopsis Number Theory 1 by : Kazuya Kato

Download or read book Number Theory 1 written by Kazuya Kato and published by American Mathematical Soc.. This book was released on 2000 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.

Introduction to $p$-adic Analytic Number Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821847740
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to $p$-adic Analytic Number Theory by : M. Ram Murty

Download or read book Introduction to $p$-adic Analytic Number Theory written by M. Ram Murty and published by American Mathematical Soc.. This book was released on 2009-02-09 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 932 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bulletin of the American Mathematical Society

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Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society

Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2002 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: