Author: Anatol N. Kirillov Publisher: World Scientific ISBN: 9789812810007 Category : Mathematics Languages : en Pages : 336
Book Description
The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop. Contents: Vanishing Theorems and Character Formulas for the Hilbert Scheme of Points in the Plane (M Haiman); Exclusion Statistics and Chiral Partition Function (K Hikami); On the Spectrum of Dehn Twists in Quantum Teichmller Theory (R Kashaev); Introduction to Tropical Combinatorics (A Kirillov); Transition on Grothendieck Polynomials (A Lascoux); Generalized HAlder''s Theorem for Multiple Gamma Function (M Nishizawa); Quantum Calogero-Moser Models: Complete Integrability for All the Root Systems (R Sasaki); Simplification of Thermodynamic BetheOCoAnsatz Equations (M Takahashi); and other papers. Readership: Researchers and graduates in mathematical physics and combinatorics & graph theory."
Author: Anatol N Kirillov Publisher: World Scientific ISBN: 9814490911 Category : Science Languages : en Pages : 329
Book Description
The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop.
Author: Bruce C. Berndt Publisher: American Mathematical Soc. ISBN: 9780821856277 Category : Mathematics Languages : en Pages : 292
Book Description
The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $ 1\psi 1$ summation theorem as ''a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings,the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.
Author: Joaquin Bustoz Publisher: Springer Science & Business Media ISBN: 9401008183 Category : Mathematics Languages : en Pages : 521
Book Description
The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.
Author: Laurent Bartholdi Publisher: Springer Science & Business Media ISBN: 9783764374464 Category : Mathematics Languages : en Pages : 432
Book Description
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.
Author: Kurusch Ebrahimi-Fard Publisher: American Mathematical Soc. ISBN: 0821853295 Category : Mathematics Languages : en Pages : 480
Book Description
This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.
Author: Piotr Pragacz Publisher: Springer Science & Business Media ISBN: 3764373423 Category : Mathematics Languages : en Pages : 321
Book Description
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis
Author: V.A. Malyshev Publisher: Springer Science & Business Media ISBN: 9401005753 Category : Science Languages : en Pages : 335
Book Description
New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Author: Mats Andersson Publisher: Birkhäuser ISBN: 3034878710 Category : Mathematics Languages : en Pages : 172
Book Description
This book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.