University Lecture Series, Volume: 46
2008; approx. 123 pp; softcover
ISBN-13: 978-0-8218-4727-5
Expected publication date is October 25, 2008.
Aperiodic tilings are interesting to mathematicians and scientists for both theoretical and practical reasons. The serious study of aperiodic tilings began as a solution to a problem in logic. Simpler aperiodic tilings eventually revealed hidden "symmetries" that were previously considered impossible, while the tilings themselves were quite striking.
The discovery of quasicrystals showed that such aperiodicity actually occurs in nature and led to advances in materials science. Many properties of aperiodic tilings can be discerned by studying one tiling at a time. However, by studying families of tilings, further properties are revealed. This broader study naturally leads to the topology of tiling spaces.
This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces.
The text contains a generous supply of examples and exercises.
Graduate students and research mathematicians interested in topology, dynamical systems, and aperiodic tilings.
Basic notions
Tiling spaces and inverse limits
Cohomology of tilings spaces
Relaxing the rules I: Rotations
Pattern-equivariant cohomology
Tricks of the trade
Relaxing the rules II: Tilings without finite local complexity
Solutions to selected exercises
Bibliography
Proceedings of Symposia in Pure Mathematics,Volume: 78
2008; 304 pp; hardcover
ISBN-13: 978-0-8218-4430-4
Expected publication date is November 7, 2008.
Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathematical ideas goes back to the works of Cecotti, Vafa, et al. around 1991 on the geometry of topological field theory. Their tt*-geometry (tt* stands for topological-antitopological) was motivated by physics, but it turned out to unify ideas from such separate branches of mathematics as singularity theory, Hodge theory, integrable systems, matrix models, and Hurwitz spaces. The interaction among these fields suggested by tt*-geometry has become a fast moving and exciting research area.
This book, loosely based on the 2007 Augsburg, Germany workshop "From tQFT to tt* and Integrability", is the perfect introduction to the range of mathematical topics relevant to tt*-geometry. It begins with several surveys of the main features of tt*-geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. The volume moves on to explorations of current foundational issues in Hodge theory: higher weight phenomena in twistor theory and non-commutative Hodge structures and their relation to mirror symmetry. The book concludes with a series of applications to integrable systems and enumerative geometry, exploring further extensions and connections to physics.
With its progression through introductory, foundational, and exploratory material, this book is an indispensable companion for anyone working in the subject or wishing to enter it.
Graduate students and research mathematicians interested in mathematical physics.
C. Sabbah -- Universal unfoldings of Laurent polynomials and tt* structures
K. Saito and A. Takahashi -- From primitive forms to Frobenius manifolds
C. Hertling and C. Sevenheck -- Twistor stuctures, $tt^*$-geometry and singularity theory
V. Cortes and L. Schafer -- Differential geometric aspects of the tt*-equations
L. Katzarkov, M. Kontsevich, and T. Pantev -- Hodge theoretic aspects of mirror symmetry
C. Simpson -- A weight two phenomenon for the moduli of rank one local systems on open varieties
L. K. Hoevenaars -- Associativity for the Neumann system
A. A. Gerasimov and S. L. Shatashvili -- Two-dimensional gauge theories and quantum integrable systems
V. Bouchard and M. Marino -- Hurwitz numbers, matrix models and enumerative geometry
A. Neitzke and J. Walcher -- Background independence and the open topological string wavefunction
Proceedings of Symposia in Pure Mathematics, Volume: 79
2008; 423 pp; hardcover
ISBN-13: 978-0-8218-4424-3
Expected publication date is November 21, 2008.
V. G. Maz'ya is widely regarded as a truly outstanding mathematician, whose work spans 50 years and covers many areas of mathematical analysis.
This volume contains a unique collection of papers contributed on the occasion of Maz'ya's 70th birthday by a distinguished group of experts of international stature in the fields of Harmonic Analysis, Partial Differential Equations, Function Theory, Spectral Analysis, and History of Mathematics, reflecting the state of the art in these areas, in which Maz'ya himself has made some of his most significant contributions.
Research mathematicians interested in partial differential equations.
N. Arcozzi, R. Rochberg, and E. Sawyer -- Capacity, Carleson measures, boundary convergence, and exceptional sets
J. Bourgain -- On the absence of dynamical localization in higher dimensional random Schrodinger operators
H. Brezis and J. Van Schaftingen -- Circulation integrals and critical Sobolev spaces: Problems of optimal constants
L. Capogna, N. Garofalo, and D.-M. Nhieu -- Mutual absolute continuity of harmonic and surface measures for Hormander type operators
L. Garding -- Soviet-Russian and Swedish mathematical contacts after the war. A personal account
F. Gesztesy and M. Mitrea -- Generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Krein-type resolvent formulas for Schrodinger operators on bounded Lipschitz domains
S. Hofmann -- A local $Tb$ theorem for square functions
J.-P. Kahane -- Partial differential equations, trigonometric series, and the concept of function around 1800: A brief story about Lagrange and Fourier
C. E. Kenig -- Quantitative unique continuation, logarithmic convexity of Gaussian means and Hardy's uncertainty principle
J. L. Lewis, N. Lundstrom, and K. Nystrom -- Boundary Harnack inequalities for operators of $p$-Laplace type in Reifenberg flat domains
M. Lilli and J. F. Toland -- Waves on a steady stream with vorticity
F. Nazarov and A. Volberg -- On analytic capacity of portions of continuum and a question of T. Murai
B. Simon -- The Christoffel-Darboux kernel
M. E. Taylor -- A saint-Venant principle for Lipschitz cylinders
H. Triebel -- Wavelets in function spaces
I. E. Verbitsky -- Weighted norm inequalities with positive and indefinite weights
M. Venouziou and G. C. Verchota -- The mixed problem for harmonic functions in polyhedra of $\mathbb{R}^3$
Contemporary Mathematics, Volume: 471
2008; 218 pp; softcover
ISBN-13: 978-0-8218-4650-6
Expected publication date is November 15, 2008.
This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and $q$-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research.
This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field.
Graduate students and research mathematicians interested in orthogonal polynomials and special functions.
C. Balderrama and W. O. Urbina R. -- Fractional integration and fractional differentiation for $d$-dimensional Jacobi expansions
K. G. Boreskov, A. V. Turbiner, and J. C. Lopez Vieyra -- Sutherland-type trigonometric models, trigonometric invariants, and multivariate polynomials
R. P. Boyer and W. M. Y. Goh -- Polynomials associated with partitions: Asymptotics and zeros
S. Chakravarty and Y. Kodama -- A generating function for the $N$-soliton solutions of the Kadomtsev-Petviashvili II equation
P. A. Clarkson -- Asymptotics of the second Painleve equation
M. W. Coffey -- Evaluation of certain Mellin transformations in terms of the trigamma and polygamma functions
D. Crowdy and J. Marshall -- Conformal maps to generalized quadrature domains
A Elbert and M. E. Muldoon -- Approximations for zeros of Hermite functions
H. Kazi and E. Neuman -- Inequalities and bounds for elliptic integrals II
R. S. Maier -- P-symbols, Heun identities, and $_3F_2$ identities
D. Manna and V. H. Moll -- An iterative method for numerical integration of rational functions
M. J. Schlosser -- A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator
S. H. Son -- Ramanujan's symmetric theta functions in his lost notebook
V. Varlamov -- Integral representations for products of Airy functions and their fractional derivatives
Contemporary Mathematics, Volume: 472
2008; 246 pp; softcover
ISBN-13: 978-0-8218-4366-6
Expected publication date is November 16, 2008.
The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature.
This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields.
Graduate students and research mathematicians interested in representations in Lie groups.
2008; approx. 339 pp; hardcover
ISBN-13: 978-0-8218-4367-3
Expected publication date is December 28, 2008.
This is a book in the tradition of Euclidean synthetic geometry written by one of the twentieth century's great mathematicians. The original audience was pre-college teachers, but it is useful as well to gifted high school students and college students, in particular, to mathematics majors interested in geometry from a more advanced standpoint.
The text starts where Euclid starts, and covers all the basics of plane Euclidean geometry. But this text does much more. It is at once pleasingly classic and surprisingly modern. The problems (more than 450 of them) are well-suited to exploration using the modern tools of dynamic geometry software. For this reason, the present edition includes a CD of dynamic solutions to select problems, created using Texas Instruments' TI-NspireTM Learning Software. The TI-NspireTM documents demonstrate connections among problems and--through the free trial software included on the CD--will allow the reader to explore and interact with Hadamard's Geometry in new ways. The material also includes introductions to several advanced topics. The exposition is spare, giving only the minimal background needed for a student to explore these topics. Much of the value of the book lies in the problems, whose solutions open worlds to the engaged reader.
And so this book is in the Socratic tradition, as well as the Euclidean, in that it demands of the reader both engagement and interaction. A forthcoming companion volume that includes solutions, extensions, and classroom activities related to the problems can only begin to open the treasures offered by this work. We are just fortunate that one of the greatest mathematical minds of recent times has made this effort to show to readers some of the opportunities that the intellectual tradition of Euclidean geometry has to offer.
Undergraduate students and professors interested in Euclidean geometry.
Introduction
On the straight line
On the circle
On similarity
Complements to book III
On areas
On the methods of geometry
On Euclid's postulate
On the problem of tangent circles
On the notion of area
Miscellaneous problems and problems proposed in various contests
Malfatti's problem