Contemporary Mathematics, Volume: 563
2012; 211 pp; softcover
ISBN-13: 978-0-8218-7584-1
This volume represents the 2010 Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia.
The papers cover the fields of Supersymmetric Quantum Mechanics and Quantum Integrable Systems, from an algebraic point of view. Some results presented in this volume correspond to the analysis of Darboux Transformations in higher order as well as some exceptional orthogonal polynomials.
Y. V. Brezhnev -- Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials
D. Dutta and P. Roy -- Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty
D. Gomez-Ullate, N. Kamran, and R. Milson -- On orthogonal polynomials spanning a non-standard flag
M. A. Gonzalez Leon, M. T. Mayado, J. M. Guilarte, and M. J. Senosiain -- On the supersymmetric spectra of two planar integrable quantum systems
Y. Grandati and A. Berard -- Solvable rational extension of translationally shape invariant potentials
V. Ovsienko -- The pentagram map: Geometry, algebra, integrability
E. G. Reyes -- Jet bundles, symmetries, Darboux transforms
A. Schulze-Halberg -- Explicit higher-dimensional Darboux transformations for the time-dependent Schrodinger equation
V. P. Spiridonov -- Elliptic beta integrals and solvable models of statistical mechanics
Contemporary Mathematics, Volume: 564
2012; 249 pp; softcover
ISBN-13: 978-0-8218-6899-7
Expected publication date is March 30, 2012.
This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia.
This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks.
Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves.
The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.
P. Hacking -- Compact moduli spaces of surfaces of general type
A.-M. Castravet and J. Tevelev -- Rigid curves on overline{M}_{0,n} and arithmetic breaks
L. Caporaso -- Algebraic and combinatorial Brill-Noether theory
J. Alper and D. Hyeon -- GIT constructions of log canonical models of overline{M}_g
S. Casalaina-Martin, D. Jensen, and R. Laza -- The geometry of the ball quotient model of the moduli space of genus four curves
E. Arbarello and G. Mondello -- Two remarks on the Weierstrass flag
N. Fakhruddin -- Chern classes of conformal blocks
V. Balaji and J. Kollar -- Restrictions of stable bundles
P. Belkale -- Orthogonal bundles, theta characteristics and symplectic strange duality
S. J. Kovacs -- The splitting principle and singularities
S. Mukai -- Igusa quartic and Steiner surfaces
M. Aprodu and G. Farkas -- Green's conjecture for general covers
B. Hassett and Y. Tschinkel -- Spaces of sections of quadric surface fibrations over curves
Contemporary Mathematics, Volume: 565
2012; 286 pp; softcover
ISBN-13: 978-0-8218-5317-7
Expected publication date is March 30, 2012.
This volume contains the proceedings of the tenth international conference on Representation Theory of Algebraic Groups and Quantum Groups, held August 2-6, 2010, at Nagoya University, Nagoya, Japan.
The survey articles and original papers contained in this volume offer a comprehensive view of current developments in the field. Among others reflecting recent trends, one central theme is research on representations in the affine case. In three articles, the authors study representations of W-algebras and affine Lie algebras at the critical level, and three other articles are related to crystals in the affine case, that is, Mirkovic-Vilonen polytopes for affine type A and Kerov-Kirillov-Reshetikhin type bijection for affine type E_6.
Other contributions cover a variety of topics such as modular representation theory of finite groups of Lie type, quantum queer super Lie algebras, Khovanov's arc algebra, Hecke algebras and cyclotomic q-Schur algebras, G_1T-Verma modules for reductive algebraic groups, equivariant K-theory of quantum vector bundles, and the cluster algebra.
T. Arakawa -- W-algebras at the critical level
R. Bezrukavnikov and Q. Lin -- Highest weight modules at the critical level and noncommutative Springer resolution
J. Brundan -- An orthogonal form for level two Hecke algebras with applications
P. Fiebig -- On the restricted projective objects in the affine category mathcal{O} at the critical level
M. Geck -- Remarks on modular representations of finite groups of Lie type in non-defining characteristic
J. H. Jung and S.-J. Kang -- Quantum queer superalgebras
M. Kaneda -- Homomorphisms between neighboring G_1T-Verma modules
G. I. Lehrer and R. B. Zhang -- Quantum group actions on rings and equivariant K-theory
S. Naito, D. Sagaki, and Y. Saito -- Toward Berenstein-Zelevinsky data in affine type A, part I: construction of the affine analogs
S. Naito, D. Sagaki, and Y. Saito -- Toward Berenstein-zelevinsky data in affine type A, part II: Explicit description
T. Nakanishi and A. Zelevinsky -- On tropical dualities in cluster algebras
M. Okado and N. Sano -- KKR type bijection for the exceptional affine algebra E_6^{(1)}
T. Shoji and N. Xi -- Iwahori's question for affine Hecke algebras
K. Wada -- On Weyl modules of cyclotomic q-Schur algebras
Student Mathematical Library, Volume: 62
2012; approx. 206 pp; softcover
ISBN-13: 978-0-8218-7392-2
Expected publication date is June 23, 2012.
What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory.
The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including relations, recursion, induction, and logical and set notation and operators. That background, along with ample explanation, examples, exercises, and suggestions for further reading, make this book ideal for independent study or courses with few prerequisites.
Undergraduate students interested in computability theory and recursion theory.
Introduction
Background
Defining computability
Working with computable functions
Computing and enumerating sets
Turing reduction and Post's problem
Two hierarchies of sets
Further tools and results
Areas of research
Mathematical asides
Bibliography
Index
Contemporary Mathematics, Volume: 567
2012; 264 pp; softcover
ISBN-13: 978-0-8218-6922-2
Expected publication date is April 19, 2012.
This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs.
Graduate students and research mathematicians interested in ergodic theory, dynamical systems, and group actions
M. Abert and G. Elek -- Hyperfinite actions on countable sets and probability measure spaces
A. B. Antonevich, V. I. Bakhtin, and A. V. Lebedev -- A road to the spectral radius of transfer operators
M. Boshernitzan -- A condition for weak mixing of induced IETs
L. Bowen -- Every countably infinite group is almost Ornstein
L. A. Bunimovich -- Fair dice-like hyperbolic systems
G. Chinta, J. Jorgenson, and A. Karlsson -- Complexity and heights of tori
A. I. Danilenko -- Flows with uncountable but meager group of self-similarities
E. Glasner and Y. Gutman -- The universal minimal space of the homeomorphism group of a H-homogeneous space
W. Huang and X. Ye -- Generic eigenvalues, generic factors and weak disjointness
E. Janvresse, T. de la Rue, and V. Ryzhikov -- Around King's rank-one theorems: Flows and mathbb{Z}^n-actions
V. A. Kaimanovich and F. Sobieczky -- Random walks on horospheric products
Y. G. Sinai -- Statistics of gaps in the sequence {sqrt{n}}
W. A. Veech -- Invariant distributions for interval exchange transformations
Y. Vorobets -- Notes on the Schreir graphs of the Grigorchuk group
B. Weiss -- Minimal models for free actions
Graduate Studies in Mathematics, Volume: 134
2012; approx. 420 pp; hardcover
ISBN-13: 978-0-8218-7577-3
Expected publication date is June 3, 2012.
The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and local behavior of arithmetic functions, an extensive study of smooth numbers, the Hardy-Ramanujan and Landau theorems, characters and the Dirichlet theorem, the abc conjecture along with some of its applications, and sieve methods. The book concludes with a whole chapter on the index of composition of an integer.
One of this book's best features is the collection of problems at the end of each chapter that have been chosen carefully to reinforce the material. The authors include solutions to the even-numbered problems, making this volume very appropriate for readers who want to test their understanding of the theory presented in the book.
Graduate students and research mathematicians interested in analytic number theory.
Preliminary notions
Prime numbers and their properties
The Riemann zeta function
Setting the stage for the proof of the prime number theorem
The proof of the prime number theorem
The global behavior of arithmetic functions
The local behavior of arithmetic functions
The fascinating Euler function
Smooth numbers
The Hardy-Ramanujan and Landau theorems
The abc conjecture and some of its applications
Sieve methods
Prime numbers in arithmetic progression
Characters and the Dirichlet theorem
Selected applications of primes in arithmetic progression
The index of composition of an integer
Appendix. Basic complex analysis theory
Solutions to even-numbered problems
Bibliography
Index