Davenport Zannier Polynomials And Dessins D Enfants

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Davenport-Zannier Polynomials and Dessins D'Enfants

NIKOLAI M. ADRIANOV;FEDOR PAKOVICH;ALEXANDER K. ZV.,Nikolai M. Adrianov,Fedor Pakovich,Aleksandr Kalmanovich Zvonkin
Davenport Zannier Polynomials and Dessins D Enfants Book PDF

Author : NIKOLAI M. ADRIANOV;FEDOR PAKOVICH;ALEXANDER K. ZV.,Nikolai M. Adrianov,Fedor Pakovich,Aleksandr Kalmanovich Zvonkin
Publisher : Unknown
Page : 187 pages
File Size : 52,6 Mb
Release : 2024-06-14
Category : Algebraic fields
ISBN : 1470460297

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Davenport-Zannier Polynomials and Dessins D'Enfants by NIKOLAI M. ADRIANOV;FEDOR PAKOVICH;ALEXANDER K. ZV.,Nikolai M. Adrianov,Fedor Pakovich,Aleksandr Kalmanovich Zvonkin Pdf

The French expression ""dessins d'enfants"" means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics. The major part of the book is quite elementary a.

Davenport–Zannier Polynomials and Dessins d’Enfants

Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin
Davenport Zannier Polynomials and Dessins d Enfants Book PDF

Author : Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 49,8 Mb
Release : 2020-06-29
Category : Education
ISBN : 9781470456344

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Davenport–Zannier Polynomials and Dessins d’Enfants by Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin Pdf

The French expression “dessins d'enfants” means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics. The major part of the book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics. The reader may either take the basic facts of these theories for granted or use our book as a motivation and a first approach to these subjects.

Asymptotic Geometric Analysis, Part II

Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Asymptotic Geometric Analysis Part II Book PDF

Author : Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Publisher : American Mathematical Society
Page : 645 pages
File Size : 41,9 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9781470463601

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Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman Pdf

This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.

Amenability of Discrete Groups by Examples

Kate Juschenko
Amenability of Discrete Groups by Examples Book PDF

Author : Kate Juschenko
Publisher : American Mathematical Society
Page : 180 pages
File Size : 54,6 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781470470326

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Amenability of Discrete Groups by Examples by Kate Juschenko Pdf

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

The Adams Spectral Sequence for Topological Modular Forms

Robert R. Bruner,John Rognes
The Adams Spectral Sequence for Topological Modular Forms Book PDF

Author : Robert R. Bruner,John Rognes
Publisher : American Mathematical Society
Page : 690 pages
File Size : 47,8 Mb
Release : 2021-12-23
Category : Mathematics
ISBN : 9781470469580

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The Adams Spectral Sequence for Topological Modular Forms by Robert R. Bruner,John Rognes Pdf

The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.

The Classification of the Finite Simple Groups, Number 9

Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon
The Classification of the Finite Simple Groups Number 9 Book PDF

Author : Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon
Publisher : American Mathematical Society
Page : 520 pages
File Size : 44,7 Mb
Release : 2021-02-22
Category : Mathematics
ISBN : 9781470464370

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The Classification of the Finite Simple Groups, Number 9 by Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon Pdf

This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.

Perverse Sheaves and Applications to Representation Theory

Pramod N. Achar
Perverse Sheaves and Applications to Representation Theory Book PDF

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 49,8 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

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Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.

Maximal Function Methods for Sobolev Spaces

Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Maximal Function Methods for Sobolev Spaces Book PDF

Author : Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 51,8 Mb
Release : 2021-08-02
Category : Education
ISBN : 9781470465759

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Maximal Function Methods for Sobolev Spaces by Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas Pdf

This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

Local Operators in Integrable Models I

Michio Jimbo,Tetsuji Miwa,Fedor Smirnov
Local Operators in Integrable Models I Book PDF

Author : Michio Jimbo,Tetsuji Miwa,Fedor Smirnov
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 50,9 Mb
Release : 2021-07-02
Category : Education
ISBN : 9781470465520

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Local Operators in Integrable Models I by Michio Jimbo,Tetsuji Miwa,Fedor Smirnov Pdf

Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.

Sampling in Combinatorial and Geometric Set Systems

Nabil H. Mustafa
Sampling in Combinatorial and Geometric Set Systems Book PDF

Author : Nabil H. Mustafa
Publisher : American Mathematical Society
Page : 251 pages
File Size : 51,5 Mb
Release : 2022-01-14
Category : Mathematics
ISBN : 9781470461560

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Sampling in Combinatorial and Geometric Set Systems by Nabil H. Mustafa Pdf

Understanding the behavior of basic sampling techniques and intrinsic geometric attributes of data is an invaluable skill that is in high demand for both graduate students and researchers in mathematics, machine learning, and theoretical computer science. The last ten years have seen significant progress in this area, with many open problems having been resolved during this time. These include optimal lower bounds for epsilon-nets for many geometric set systems, the use of shallow-cell complexity to unify proofs, simpler and more efficient algorithms, and the use of epsilon-approximations for construction of coresets, to name a few. This book presents a thorough treatment of these probabilistic, combinatorial, and geometric methods, as well as their combinatorial and algorithmic applications. It also revisits classical results, but with new and more elegant proofs. While mathematical maturity will certainly help in appreciating the ideas presented here, only a basic familiarity with discrete mathematics, probability, and combinatorics is required to understand the material.

Linear and Quasilinear Parabolic Systems: Sobolev Space Theory

David Hoff
Linear and Quasilinear Parabolic Systems Sobolev Space Theory Book PDF

Author : David Hoff
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 40,9 Mb
Release : 2020-11-18
Category : Education
ISBN : 9781470461614

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Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by David Hoff Pdf

This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.

Completion Problems on Operator Matrices

Dragana S. Cvetković Ilić
Completion Problems on Operator Matrices Book PDF

Author : Dragana S. Cvetković Ilić
Publisher : American Mathematical Society
Page : 170 pages
File Size : 54,7 Mb
Release : 2022-06-07
Category : Mathematics
ISBN : 9781470469870

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Completion Problems on Operator Matrices by Dragana S. Cvetković Ilić Pdf

Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.

Numerical Algorithms for Number Theory: Using Pari/GP

Karim Belabas,Henri Cohen
Numerical Algorithms for Number Theory Using Pari GP Book PDF

Author : Karim Belabas,Henri Cohen
Publisher : American Mathematical Soc.
Page : 429 pages
File Size : 54,6 Mb
Release : 2021-06-23
Category : Education
ISBN : 9781470463519

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Numerical Algorithms for Number Theory: Using Pari/GP by Karim Belabas,Henri Cohen Pdf

This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

Inverse Problems and Zero Forcing for Graphs

Leslie Hogben,Jephian C.-H. Lin,Bryan L. Shader
Inverse Problems and Zero Forcing for Graphs Book PDF

Author : Leslie Hogben,Jephian C.-H. Lin,Bryan L. Shader
Publisher : American Mathematical Society
Page : 302 pages
File Size : 46,5 Mb
Release : 2022-07-21
Category : Mathematics
ISBN : 9781470466558

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Inverse Problems and Zero Forcing for Graphs by Leslie Hogben,Jephian C.-H. Lin,Bryan L. Shader Pdf

This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.

One-Dimensional Turbulence and the Stochastic Burgers Equation

Alexandre Boritchev,Sergei Kuksin
One Dimensional Turbulence and the Stochastic Burgers Equation Book PDF

Author : Alexandre Boritchev,Sergei Kuksin
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 45,6 Mb
Release : 2021-07-01
Category : Education
ISBN : 9781470464363

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One-Dimensional Turbulence and the Stochastic Burgers Equation by Alexandre Boritchev,Sergei Kuksin Pdf

This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers equation with small viscosity under periodic boundary conditions and to interpreting the obtained results in terms of one-dimensional turbulence in a fictitious one-dimensional fluid described by the Burgers equation. The properties of one-dimensional turbulence which we rigorously derive are then compared with the heuristic Kolmogorov theory of hydrodynamical turbulence, known as the K41 theory. It is shown, in particular, that these properties imply natural one-dimensional analogues of three principal laws of the K41 theory: the size of the Kolmogorov inner scale, the 2/3 2/3-law, and the Kolmogorov–Obukhov law. The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L 1 L1-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.