Special Functions Kz Type Equations And Representation Theory

Author : Aleksandr Nikolaevich Varchenko
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 46,8 Mb
Release : 2003
Category : Functions, Special
ISBN : 9780821828670

Get Book

Special Functions, KZ Type Equations, and Representation Theory by Aleksandr Nikolaevich Varchenko Pdf

The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its sqs-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra s\mathfrak{sl 2s. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.

Author : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
Page : 628 pages
File Size : 44,9 Mb
Release : 1978
Category : Mathematics
ISBN : 0821886525

Get Book

Special Functions and the Theory of Group Representations by Naum I͡Akovlevich Vilenkin Pdf

Author : Denis Ibadula,Willem Veys
Publisher : Springer
Page : 295 pages
File Size : 41,6 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9783319091860

Get Book

Bridging Algebra, Geometry, and Topology by Denis Ibadula,Willem Veys Pdf

Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

Author : Wen-Ching Winnie Li
Publisher : American Mathematical Soc.
Page : 95 pages
File Size : 53,9 Mb
Release : 2019-03-01
Category : Combinatorial number theory
ISBN : 9781470449001

Get Book

Zeta and L -functions in Number Theory and Combinatorics by Wen-Ching Winnie Li Pdf

Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

Author : Erik Koelink,Stefan Kolb,Nicolai Reshetikhin,Bart Vlaar
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 40,7 Mb
Release : 2022-08-30
Category : Education
ISBN : 9781470465209

Get Book

Hypergeometry, Integrability and Lie Theory by Erik Koelink,Stefan Kolb,Nicolai Reshetikhin,Bart Vlaar Pdf

This volume contains the proceedings of the virtual conference on Hypergeometry, Integrability and Lie Theory, held from December 7–11, 2020, which was dedicated to the 50th birthday of Jasper Stokman. The papers represent recent developments in the areas of representation theory, quantum integrable systems and special functions of hypergeometric type.

Author : Charles Fefferman,Arie Israel
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 40,8 Mb
Release : 2020-10-27
Category : Education
ISBN : 9781470461300

Get Book

Fitting Smooth Functions to Data by Charles Fefferman,Arie Israel Pdf

This book is an introductory text that charts the recent developments in the area of Whitney-type extension problems and the mathematical aspects of interpolation of data. It provides a detailed tour of a new and active area of mathematical research. In each section, the authors focus on a different key insight in the theory. The book motivates the more technical aspects of the theory through a set of illustrative examples. The results include the solution of Whitney's problem, an efficient algorithm for a finite version, and analogues for Hölder and Sobolev spaces in place of Cm. The target audience consists of graduate students and junior faculty in mathematics and computer science who are familiar with point set topology, as well as measure and integration theory. The book is based on lectures presented at the CBMS regional workshop held at the University of Texas at Austin in the summer of 2019.

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 43,6 Mb
Release : 2019-08-23
Category : Algebraic topology
ISBN : 9781470452063

Get Book

Lectures on Field Theory and Topology by Daniel S. Freed Pdf

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Author : Davar Khoshnevisan
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 52,8 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9781470415471

Get Book

Analysis of Stochastic Partial Differential Equations by Davar Khoshnevisan Pdf

The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.

Author : Richard Beals,Roderick Wong
Publisher : Cambridge University Press
Page : 489 pages
File Size : 45,9 Mb
Release : 2016-05-17
Category : Mathematics
ISBN : 9781107106987

Get Book

Special Functions and Orthogonal Polynomials by Richard Beals,Roderick Wong Pdf

A comprehensive graduate-level introduction to classical and contemporary aspects of special functions.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 40,7 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821889508

Get Book

Nonlinear Dispersive Equations by Terence Tao Pdf

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Author : David A. Cox
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 51,9 Mb
Release : 2020-03-02
Category : Education
ISBN : 9781470451370

Get Book

Applications of Polynomial Systems by David A. Cox Pdf

Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.

Author : Alice Guionnet
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 47,8 Mb
Release : 2019-04-29
Category : Green's functions
ISBN : 9781470450274

Get Book

Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations by Alice Guionnet Pdf

Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.

Author : Semyon Alesker
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 49,9 Mb
Release : 2018-06-27
Category : Graph labelings
ISBN : 9781470443597

Get Book

Introduction to the Theory of Valuations by Semyon Alesker Pdf

Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translation-invariant continuous valuations, some of which turn out to be useful in integral geometry. This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.

Author : Ron Graham, Steve Butler
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 42,7 Mb
Release : 2015-10-01
Category : Combinatorial analysis
ISBN : 9780821841563

Get Book

Rudiments of Ramsey Theory by Ron Graham, Steve Butler Pdf

In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory. Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results. A co-publication of the AMS and CBMS.

Author : J.M. Landsberg
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 40,8 Mb
Release : 2019-07-05
Category : Calculus of tensors
ISBN : 9781470451363

Get Book

Tensors: Asymptotic Geometry and Developments 2016–2018 by J.M. Landsberg Pdf

Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication. Numerous open problems appropriate for graduate students and post-docs are included throughout.