Combinatorial Aspect Of Integrable Systems

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Combinatorial Aspect of Integrable Systems

Author : Arkady Berenstein
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Combinatorial Aspect of Integrable Systems by : Arkady Berenstein

Download or read book Combinatorial Aspect of Integrable Systems written by Arkady Berenstein and published by . This book was released on 2007 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of six papers based on the expository lectures of the workshop "Combinatorial Aspect of Integrable Systems" held at RIMS during July 26-30, 2004, as a part of the Project Research 2004 "Method of Algebraic Analysis in Integrable Systems". The topics range over crystal bases of quantum groups, its algebra-geometric analogue known as geometric crystal, generalizations of Robinson-Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang-Baxter maps, and integrable discrete dynamics. All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory

Author : Vyjayanthi Chari
Publisher : American Mathematical Soc.
ISBN 13 : 0821890379
Total Pages : 222 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory by : Vyjayanthi Chari

Download or read book Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory written by Vyjayanthi Chari and published by American Mathematical Soc.. This book was released on 2013-11-25 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, USA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.

Algebraic and Geometric Aspects of Integrable Systems and Random Matrices

Author : Anton Dzhamay
Publisher : American Mathematical Soc.
ISBN 13 : 0821887475
Total Pages : 363 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Geometric Aspects of Integrable Systems and Random Matrices by : Anton Dzhamay

Download or read book Algebraic and Geometric Aspects of Integrable Systems and Random Matrices written by Anton Dzhamay and published by American Mathematical Soc.. This book was released on 2013-06-26 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates

KP Solitons and the Grassmannians

Author : Yuji Kodama
Publisher : Springer
ISBN 13 : 981104094X
Total Pages : 138 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis KP Solitons and the Grassmannians by : Yuji Kodama

Download or read book KP Solitons and the Grassmannians written by Yuji Kodama and published by Springer. This book was released on 2017-03-24 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of the combinatorial aspect of the TNN Grassmannians and their parameterizations, which will be useful for solving the classification problem. This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. It can serve as a valuable reference for an expert, a textbook for a special topics graduate course, or a source for independent study projects for advanced upper-level undergraduates specializing in physics and mathematics.

Algebraic and Combinatorial Aspects of Tropical Geometry

Author : Erwan Brugalle
Publisher : American Mathematical Soc.
ISBN 13 : 0821891464
Total Pages : 363 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Combinatorial Aspects of Tropical Geometry by : Erwan Brugalle

Download or read book Algebraic and Combinatorial Aspects of Tropical Geometry written by Erwan Brugalle and published by American Mathematical Soc.. This book was released on 2013-05-23 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mat

New Trends in Quantum Integrable Systems

Author : Boris Feigin
Publisher : World Scientific
ISBN 13 : 9814324361
Total Pages : 517 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis New Trends in Quantum Integrable Systems by : Boris Feigin

Download or read book New Trends in Quantum Integrable Systems written by Boris Feigin and published by World Scientific. This book was released on 2010-10-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Global Aspects of Classical Integrable Systems

Author : Richard H. Cushman
Publisher : Springer Science & Business Media
ISBN 13 : 9783764354855
Total Pages : 466 pages
Book Rating : 4.3/5 (548 download)

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Book Synopsis Global Aspects of Classical Integrable Systems by : Richard H. Cushman

Download or read book Global Aspects of Classical Integrable Systems written by Richard H. Cushman and published by Springer Science & Business Media. This book was released on 1997 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete global geometric description of the motion of the two di mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top. These classical integrable Hamiltonian systems one sees treated in almost every physics book on classical mechanics. So why is this book necessary? The answer is that the standard treatments are not complete. For instance in physics books one cannot see the monodromy in the spherical pendulum from its explicit solution in terms of elliptic functions nor can one read off from the explicit solution the fact that a tennis racket makes a near half twist when it is tossed so as to spin nearly about its intermediate axis. Modem mathematics books on mechanics do not use the symplectic geometric tools they develop to treat the qualitative features of these problems either. One reason for this is that their basic tool for removing symmetries of Hamiltonian systems, called regular reduction, is not general enough to handle removal of the symmetries which occur in the spherical pendulum or in the Lagrange top. For these symmetries one needs singular reduction. Another reason is that the obstructions to making local action angle coordinates global such as monodromy were not known when these works were written.

New Trends in Quantum Integrable Systems

Author : Boris Feigin
Publisher : World Scientific
ISBN 13 : 9814462926
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis New Trends in Quantum Integrable Systems by : Boris Feigin

Download or read book New Trends in Quantum Integrable Systems written by Boris Feigin and published by World Scientific. This book was released on 2014-05-14 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto Japan from 27 to 31 July 2009. As a continuation of the RIMS Research Project a Method of Algebraic Analysis in Integrable Systemsa in 2004 the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models integrable models in quantum field theory conformal field theory mathematical aspects of Bethe ansatz special functions and integrable differential/difference equations representation theory of infinite dimensional algebras integrable models and combinatorics.Through these topics the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics."

Symmetries, Integrable Systems and Representations

Author : Kenji Iohara
Publisher : Springer
ISBN 13 : 9781447148647
Total Pages : 638 pages
Book Rating : 4.1/5 (486 download)

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Book Synopsis Symmetries, Integrable Systems and Representations by : Kenji Iohara

Download or read book Symmetries, Integrable Systems and Representations written by Kenji Iohara and published by Springer. This book was released on 2012-12-05 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : American Mathematical Society
ISBN 13 : 1470474565
Total Pages : 432 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Society. This book was released on 2023-09-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

Representation Theory, Mathematical Physics, and Integrable Systems

Author : Anton Alekseev
Publisher : Springer Nature
ISBN 13 : 3030781488
Total Pages : 652 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Representation Theory, Mathematical Physics, and Integrable Systems by : Anton Alekseev

Download or read book Representation Theory, Mathematical Physics, and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Integrable and Superintegrable Systems

Author : Boris A. Kupershmidt
Publisher : World Scientific
ISBN 13 : 9789810203160
Total Pages : 402 pages
Book Rating : 4.2/5 (31 download)

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Book Synopsis Integrable and Superintegrable Systems by : Boris A. Kupershmidt

Download or read book Integrable and Superintegrable Systems written by Boris A. Kupershmidt and published by World Scientific. This book was released on 1990 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Author : David Carfi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891480
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : David Carfi

Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

Recent Advances in Real Complexity and Computation

Author : Luis M. Pardo
Publisher : American Mathematical Soc.
ISBN 13 : 0821891502
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Real Complexity and Computation by : Luis M. Pardo

Download or read book Recent Advances in Real Complexity and Computation written by Luis M. Pardo and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.

Recent Trends in Nonlinear Partial Differential Equations

Author : Patrizia Pucci
Publisher : American Mathematical Soc.
ISBN 13 : 0821898612
Total Pages : 340 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Trends in Nonlinear Partial Differential Equations by : Patrizia Pucci

Download or read book Recent Trends in Nonlinear Partial Differential Equations written by Patrizia Pucci and published by American Mathematical Soc.. This book was released on 2013 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes that contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide ranging influence of Patrizia Pucci on the field of nonlinear analysis and partial differential equations. In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume. The companion volume (Contemporary Mathematics, Volume 594) is devoted to evolution problems in nonlinear partial differential equations.

Recent Trends in Nonlinear Partial Differential Equations I

Author : James B. Serrin
Publisher : American Mathematical Soc.
ISBN 13 : 082188736X
Total Pages : 323 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Trends in Nonlinear Partial Differential Equations I by : James B. Serrin

Download or read book Recent Trends in Nonlinear Partial Differential Equations I written by James B. Serrin and published by American Mathematical Soc.. This book was released on 2013-07-22 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t

Ring Theory and Its Applications

Author : Dinh Van Huynh
Publisher : American Mathematical Soc.
ISBN 13 : 0821887971
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Ring Theory and Its Applications by : Dinh Van Huynh

Download or read book Ring Theory and Its Applications written by Dinh Van Huynh and published by American Mathematical Soc.. This book was released on 2014-02-21 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.