Multivariable Orthogonal Polynomials And Quantum Grassmanniams Ie Grassmannians

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Grassmannian Geometry of Scattering Amplitudes

Author : Nima Arkani-Hamed
Publisher : Cambridge University Press
ISBN 13 : 1316571645
Total Pages : 205 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Grassmannian Geometry of Scattering Amplitudes by : Nima Arkani-Hamed

Download or read book Grassmannian Geometry of Scattering Amplitudes written by Nima Arkani-Hamed and published by Cambridge University Press. This book was released on 2016-05-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.

Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Author : Jianxun Hu
Publisher : Springer Nature
ISBN 13 : 9811574510
Total Pages : 367 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Schubert Calculus and Its Applications in Combinatorics and Representation Theory by : Jianxun Hu

Download or read book Schubert Calculus and Its Applications in Combinatorics and Representation Theory written by Jianxun Hu and published by Springer Nature. This book was released on 2020-10-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.

The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics

Author : James Haglund
Publisher : American Mathematical Soc.
ISBN 13 : 0821844113
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics by : James Haglund

Download or read book The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics written by James Haglund and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.

Multivariable Orthogonal Polynomials and Quantum Grassmanniams [i.e. Grassmannians]

Author : Jasper V. Stokman
Publisher :
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Multivariable Orthogonal Polynomials and Quantum Grassmanniams [i.e. Grassmannians] by : Jasper V. Stokman

Download or read book Multivariable Orthogonal Polynomials and Quantum Grassmanniams [i.e. Grassmannians] written by Jasper V. Stokman and published by . This book was released on 2001 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Foundations of Computational Mathematics

Author : Ronald A. DeVore
Publisher : Cambridge University Press
ISBN 13 : 9780521003490
Total Pages : 418 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Foundations of Computational Mathematics by : Ronald A. DeVore

Download or read book Foundations of Computational Mathematics written by Ronald A. DeVore and published by Cambridge University Press. This book was released on 2001-05-17 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.

Quantum Groups and Quantum Cohomology

Author : Davesh Maulik
Publisher :
ISBN 13 : 9782856299005
Total Pages : 209 pages
Book Rating : 4.2/5 (99 download)

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Book Synopsis Quantum Groups and Quantum Cohomology by : Davesh Maulik

Download or read book Quantum Groups and Quantum Cohomology written by Davesh Maulik and published by . This book was released on 2019 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Alice and Bob Meet Banach

Author : Guillaume Aubrun
Publisher : American Mathematical Society
ISBN 13 : 1470477963
Total Pages : 439 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Alice and Bob Meet Banach by : Guillaume Aubrun

Download or read book Alice and Bob Meet Banach written by Guillaume Aubrun and published by American Mathematical Society. This book was released on 2024-07-29 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.

Finite Frames

Author : Peter G. Casazza
Publisher : Springer Science & Business Media
ISBN 13 : 0817683739
Total Pages : 492 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Finite Frames by : Peter G. Casazza

Download or read book Finite Frames written by Peter G. Casazza and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.

Mathematics for Physics

Author : Michael Stone
Publisher : Cambridge University Press
ISBN 13 : 1139480618
Total Pages : 821 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Mathematics for Physics by : Michael Stone

Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Differentiable Measures and the Malliavin Calculus

Author : Vladimir Igorevich Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 082184993X
Total Pages : 506 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differentiable Measures and the Malliavin Calculus by : Vladimir Igorevich Bogachev

Download or read book Differentiable Measures and the Malliavin Calculus written by Vladimir Igorevich Bogachev and published by American Mathematical Soc.. This book was released on 2010-07-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Affine Insertion and Pieri Rules for the Affine Grassmannian

Author : Thomas Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821846582
Total Pages : 103 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Affine Insertion and Pieri Rules for the Affine Grassmannian by : Thomas Lam

Download or read book Affine Insertion and Pieri Rules for the Affine Grassmannian written by Thomas Lam and published by American Mathematical Soc.. This book was released on 2010 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.

Quantum Field Theory and Statistical Mechanics

Author : James Glimm
Publisher : Springer Science & Business Media
ISBN 13 : 9780817632755
Total Pages : 430 pages
Book Rating : 4.6/5 (327 download)

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Book Synopsis Quantum Field Theory and Statistical Mechanics by : James Glimm

Download or read book Quantum Field Theory and Statistical Mechanics written by James Glimm and published by Springer Science & Business Media. This book was released on 1985-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.

Coding Theory, Cryptography and Related Areas

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 9783540662488
Total Pages : 276 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Coding Theory, Cryptography and Related Areas by : Johannes Buchmann

Download or read book Coding Theory, Cryptography and Related Areas written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 1999-11-23 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.

Black Holes in Higher Dimensions

Author : Gary T. Horowitz
Publisher : Cambridge University Press
ISBN 13 : 1107013453
Total Pages : 437 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Black Holes in Higher Dimensions by : Gary T. Horowitz

Download or read book Black Holes in Higher Dimensions written by Gary T. Horowitz and published by Cambridge University Press. This book was released on 2012-04-19 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book devoted to black holes in more than four dimensions, for graduate students and researchers.

Approximate Commutative Algebra

Author : Lorenzo Robbiano
Publisher : Springer Science & Business Media
ISBN 13 : 3211993142
Total Pages : 237 pages
Book Rating : 4.2/5 (119 download)

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Book Synopsis Approximate Commutative Algebra by : Lorenzo Robbiano

Download or read book Approximate Commutative Algebra written by Lorenzo Robbiano and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.

Number Theory and Physics

Author : Jean-Marc Luck
Publisher : Springer Science & Business Media
ISBN 13 : 3642754058
Total Pages : 324 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Number Theory and Physics by : Jean-Marc Luck

Download or read book Number Theory and Physics written by Jean-Marc Luck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p adic numbers in a remarkable way.