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Author : Carol H. Chang
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.:/5 (318 download)
Download or read book Geometric Interpretations of the Macdonald Polynomials and the N! Conjecture written by Carol H. Chang and published by . This book was released on 1998 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Haglund
Publisher : American Mathematical Soc.
ISBN 13 : 0821844113
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Ian Grant Macdonald
Publisher : Oxford University Press
ISBN 13 : 9780198504504
Total Pages : 496 pages
Book Rating : 4.5/5 (45 download)
Download or read book Symmetric Functions and Hall Polynomials written by Ian Grant Macdonald and published by Oxford University Press. This book was released on 1998 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and so on. Macdonald polynomials have become a part of basic material that a researcher simply must know if (s)he wants to work in one of the above domains, ensuring this new edition will appeal to a very broad mathematical audience. Featuring a new foreword by Professor Richard Stanley of MIT.
Author : I. G. Macdonald
Publisher : Cambridge University Press
ISBN 13 : 9780521824729
Total Pages : 200 pages
Book Rating : 4.8/5 (247 download)
Download or read book Affine Hecke Algebras and Orthogonal Polynomials written by I. G. Macdonald and published by Cambridge University Press. This book was released on 2003-03-20 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Author : Louis J. Billera
Publisher : Cambridge University Press
ISBN 13 : 9780521770873
Total Pages : 360 pages
Book Rating : 4.7/5 (78 download)
Download or read book New Perspectives in Algebraic Combinatorics written by Louis J. Billera and published by Cambridge University Press. This book was released on 1999-09-28 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.
Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821891707
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)
Download or read book Perspectives in Representation Theory written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2014-03-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Perspectives in Representation Theory, held from May 12-17, 2012, at Yale University, in honor of Igor Frenkel's 60th birthday. The aim of the conference was to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and -adic groups, and quantum gauge theories. The papers in this volume present representation theory connections to numerous other subjects, as well as some of the most recent advances in representation theory, including those which occurred thanks to the application of techniques in other areas of mathematics, and of ideas of quantum field theory and string theory.
Author : Bruce E. Sagan
Publisher : Springer Science & Business Media
ISBN 13 : 1475768044
Total Pages : 254 pages
Book Rating : 4.4/5 (757 download)
Download or read book The Symmetric Group written by Bruce E. Sagan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH
Author :
Publisher :
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.3/5 (91 download)
Download or read book Methods and Applications of Analysis written by and published by . This book was released on 1999 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel I. Etingof
Publisher : European Mathematical Society
ISBN 13 : 9783037190340
Total Pages : 108 pages
Book Rating : 4.1/5 (93 download)
Download or read book Calogero-Moser Systems and Representation Theory written by Pavel I. Etingof and published by European Mathematical Society. This book was released on 2007 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, the author gives short introductions to each of the subjects involved and provides a number of exercises.
Author : Morris Marden
Publisher : American Mathematical Soc.
ISBN 13 : 0821815032
Total Pages : 260 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometry of Polynomials written by Morris Marden and published by American Mathematical Soc.. This book was released on 1949-12-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.
Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 0387226397
Total Pages : 265 pages
Book Rating : 4.3/5 (872 download)
Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Author : Matthias Beck
Publisher : American Mathematical Soc.
ISBN 13 : 147042200X
Total Pages : 325 pages
Book Rating : 4.4/5 (74 download)
Download or read book Combinatorial Reciprocity Theorems written by Matthias Beck and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
Author : Igor Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 9780521525480
Total Pages : 244 pages
Book Rating : 4.5/5 (254 download)
Download or read book Lectures on Invariant Theory written by Igor Dolgachev and published by Cambridge University Press. This book was released on 2003-08-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
Author :
Publisher :
ISBN 13 :
Total Pages : 898 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1999 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Francois Bergeron
Publisher : CRC Press
ISBN 13 : 1439865078
Total Pages : 227 pages
Book Rating : 4.4/5 (398 download)
Download or read book Algebraic Combinatorics and Coinvariant Spaces written by Francois Bergeron and published by CRC Press. This book was released on 2009-07-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and
Author : Krishnaswami Alladi
Publisher : Springer Nature
ISBN 13 : 3030570509
Total Pages : 810 pages
Book Rating : 4.0/5 (35 download)
Download or read book George E. Andrews 80 Years of Combinatory Analysis written by Krishnaswami Alladi and published by Springer Nature. This book was released on 2021-02-10 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.
Author : Jianxun Hu
Publisher : Springer Nature
ISBN 13 : 9811574510
Total Pages : 367 pages
Book Rating : 4.8/5 (115 download)
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.
