Edited by: Jens G. Christensen, Colgate University, Hamilton, NY, Susanna Dann, Vienna University of Technology, Wien, Austria, Azita Mayeli, Queensborough Community College, CUNY, Bayside, NY, and Gestur Olafsson, Louisiana State University, Baton Rouge, LA

Trends in Harmonic Analysis and Its Applications

Contemporary Mathematics, Volume: 650
2015; 209 pp; softcover
ISBN-13: 978-1-4704-1879-3

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD.

It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups.

Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.


Graduate students and research mathematicians interested in harmonic analysis, frame theory, and functional analysis.

Table of Contents

Frame theory

S. Bahmanpour, J. Cahill, P. G. Casazza, J. Jasper, and L. M. Woodland -- Phase retrieval and norm retrieval
R. Balan and D. Zou -- On Lipschitz inversion of nonlinear redundant representations
J. Cahill, P. G. Casazza, M. Ehler, and S. Li -- Tight and random nonorthogonal fusion frames
V. Oussa -- Decompositions of rational Gabor representations

Functional analysis and C?-algebras

S. Bezuglyi and P. E. T. Jorgensen -- Representations of Cuntz-Krieger relations, dynamics on Bratteli diagrams, and path-space measures
M. Dawson and G. Olafsson -- A survey of amenability theory for direct-limit groups
F. Latremoliere and J. A. Packer -- Explicit construction of equivalence bimodules between noncommutative solenoids

Harmonic analysis on manifolds

V. M. Ho and G. Olafsson -- An application of hypergeometric shift operators to the -spherical Fourier transform
P. E. T. Jorgensen, S. Pedersen, and F. Tian -- Harmonic analysis of a class of reproducing kernel Hilbert spaces arising from groups
I. Z. Pesenson -- Approximations in Lp-norms and Besov spaces on compact manifolds

Edited by: Anton Dzhamay, University of Northern Colorado, Greeley, CO, Kenichi Maruno, University of Texas-Pan American, Edinburg, TX, and Christopher M. Ormerod, California Institute of Technology, Pasadena, CA

Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations

Contemporary Mathematics, Volume: 651
2015; 194 pp; softcover
ISBN-13: 978-1-4704-1654-6

This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD.

The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory.

Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painleve equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.


Graduate students and research mathematicians interested in integrable systems.

Table of Contents

M. Noumi -- Pade interpolation and hypergeometric series
T. Suzuki -- A q-analogue of the Drinfeld-Sokolov hierarchy of type A and q-Painleve system
H. Nagoya -- Fractional calculus of quantum Painleve systems of type A(1)1
C. M. Ormerod -- Spectral curves and discrete Painleve equations
A. Dzhamay and T. Takenawa -- Geometric analysis of reductions from Schlesinger transformations to difference Painleve equations
I. Rumanov -- Beta ensembles, quantum Painleve equations and isomonodromy systems
B. Prinari and F. Vitale -- Inverse scattering transform for the focusing nonlinear Schrodinger equation with a one-sided non-zero boundary condition

David Mumford, Brown University, Providence, RI, and Tadao Oda, Tohoku University, Japan

Algebraic Geometry II

Hindustan Book Agency
2015; 516 pp; hardcover
ISBN-13: 978-93-80250-80-9
Expected publication date is December 15, 2015.

Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book", which contains notes of his lectures at Harvard University. Their genesis and evolution are described by Mumford in the preface:

Initially, notes to the course were mimeographed and bound and sold by the Harvard mathematics department with a red cover. These old notes were picked up by Springer and are now sold as The Red Book of Varieties and Schemes. However, every time I taught the course, the content changed and grew. I had aimed to eventually publish more polished notes in three volumes ...

This book contains what Mumford had then intended to be Volume II. It covers the material in the "Red Book" in more depth, with several topics added. Mumford has revised the notes in collaboration with Tadao Oda.

The book is a sequel to Algebraic Geometry I, published by Springer-Verlag in 1976.


Anyone interested in algebraic geometry.

Table of Contents

Schemes and sheaves: definitions
Exploring the world of schemes
Elementary global study of Proj R
Ground fields and base rings
Singular vs. non-singular
Group schemes and applications
The cohomology of coherent sheaves
Applications of cohomology
Two deeper results

Alberto Torchinsky, Indiana University, Bloominton, IN

Problems in Real and Functional Analysis

Graduate Studies in Mathematics, Volume: 166
2015; 467 pp; hardcover
ISBN-13: 978-1-4704-2057-4

It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems.

The Problem chapters are accompanied by Solution chapters, which include solutions to two-thirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most "natural" rather than the most elegant solution is presented.


Graduate students and researchers interested in learning and teaching real and functional analysis at the graduate level.

Table of contents

Edited by: Koryo Miura, University of Tokyo, Japan, Toshikazu Kawasaki, Anan National College of Technology, Tokushima, Japan, Tomohiro Tachi, University of Tokyo, Japan, Ryuhei Uehara, Japan Advanced Institute of Science and Technology, Ishikawa, Japan, Robert J. Lang, Langorigami, Alamo, CA, and Patsy Wang-Iverson, Gabriella & Paul Rosenbaum Foundation, Bryn Mawr, PA


approx. 736 pp; softcover
ISBN-13: 978-1-4704-1874-8

Origami6 is a unique collection of papers illustrating the connections between origami and a wide range of fields. The papers compiled in this two-part set were presented at the 6th International Meeting on Origami in Science, Mathematics and Education (10-13 August 2014, Tokyo, Japan). They display the creative melding of origami (or, more broadly, folding) with fields ranging from cell biology to space exploration, from education to kinematics, from abstract mathematical laws to the artistic and aesthetics of sculptural design.

This two-part book contains papers accessible to a wide audience, including those interested in art, design, history, and education and researchers interested in the connections between origami and science, technology, engineering, and mathematics. Part 1 contains papers on various aspects of mathematics of origami: coloring, constructability, rigid foldability, and design algorithms. Part 2 focuses on the connections between origami and more applied areas of science: engineering, physics, architecture, industrial design, and other artistic fields that go well beyond the usual folded paper.


Undergraduate and graduate students and research mathematicians interested in origami and applications in mathematics, technology, art, and education.

Table of Contents

Part 1
Mathematics of origami: Coloring

T. C. Hull -- Coloring connections with counting mountain-valley assignments
M. L. A. de las Penas, E. C. Taganap, and T. A. Rapanut -- Color symmetry approach to the construction of crystallographic flat origami
s.-m. Belcastro and T. C. Hull -- Symmetric colorings of polypolyhedra

Mathematics of origami: constructibility

J. Guardia and E. Tramuns -- Geometric and arithmetic relations concerning origami
J. I. Royo Prieto and E. Tramuns -- Abelian and non-abelian numbers via 3D origami
F. Ghourabi, T. Ida, and K. Takahashi -- Interactive construction and automated proof in Eos system with application to knot fold of regular polygons
S. Chen -- Equal division on any polygon side by folding
R. Uehara -- A survey and recent results about commmon developments of two or more boxes
H. A. Akitaya, Y. Kanamori, Y. Fukui, and J. Mitani -- Unfolding simple folds from crease patterns

Mathematics of origami: Rigid foldability

T. Tachi -- Rigid folding of periodic origami tessellations
Z. Abel, R. Connelly, E. Demaine, M. L. Demaine, T. C. Hull, A. Lubiw, and T. Tachi -- Rigid flattening of polyhedra with slits
T. A. Evans, R. J. Lang, S. P. Magleby, and L. L. Howell -- Rigidly foldable origami twists
Z. Abel, T. C. Hull, and T. Tachi -- Locked rigid origami with multiple degrees of freedom
K. Zhang, C. Qiu, and J. S. Dai -- Screw-algebra-based kinematic and static modeling of origami-inspired mechanisms
B. J. Edmondson, R. J. Lang, M. R. Morgan, S. P. Magleby, and L. L. Howell -- Thick rigidly foldable structures realized by an offset panel technique
J. S. Dai -- Configuration transformation and manipulation of origami cartons

Mathematics of origami: design algorithms

E. D. Demaine and J. S. Ku -- Filling a hole in a crease pattern: Isometric mapping from prescribed boundary folding
R. J. Lang -- Spiderwebs, tilings, and flagstone tessellations
E. D. Demaine, M. L. Demaine, and K. Qaiser -- Scaling any surface down to any fraction
E. D. Demaine, M. L. Demaine, D. A. Huffmann, D. Koschitz, and T. Tachi -- Characterization of curved creases and rulings: Design and analysis of lens tessellations
S. Chandra, S. Bhooshan, and M. El-Sayed -- Curve-folding polyhedra skeletons through smoothing
T. Sushida, A. Huzume, and Y. Yamagishi -- Design methods of origami tessellations for triangular spiral multiple tilings
T. R. Crain -- A new scheme to describe twist-fold tessellations
E. Davis, E. D. Demaine, M. L. Demaine, and J. Ramseyer -- Weaving a uniformly thick sheet from rectangles
H. Y. Cheng -- Extruding towers by serially grafting prismoids
G. Konjevod -- On pleat rearrangements in pureland tessellations
R. J. Lang and R. C. Alperin -- Graph paper for polygon-packed origami design
T. Kawasaki -- A method to fold generalized bird bases from a given quadrilateral containing an inscribed circle
R. J. Lang and B. Hayes -- Pentasia: An aperiodic origami surface
U. Ikegami -- Base design of a snowflake curve model and its difficulties
M. Kawamura -- Two calculations for geodesic modular works

Part 2
Mathematics of origami

Y. Klett, M. Grzeschik, and P. Middenhorf -- Comparison of compressive properties of periodic non-flat tessellations
K. Fuchi, P. R. Buskohl, J. J. Joo, G. W. Reich, and R. A. Vaia -- Numerical analysis of origami structures through modified frame elements
Y. Yang, X. Zhao, S. Tokura, and I. Hagiwara -- A study on crash energy absorption ability of lightweight structures with truss core panel
E. T. Filipov, T. Tachi, and G. H. Paulino -- Toward optimization of stiffness and flexibility of rigid, flat-foldable origami structures
J. M. Gattas and Z. You -- Structural engineering applications of morphing sandwich structures
S. Ishida, H. Morimura, and I. Hagiwara -- Sound-insulting performance of origami-based sandwich trusscore panels
J. Ho and Z. You -- Thin-walled deployable grid structures
R. Maleczek -- Deployable linear folded stripe structures
G. H. Filz, G. Grasser, J. Ladinig, and R. Maleczek -- Gravity and friction-driven self-organized folding
E. Iwase and I. Shimoyama -- Magnetic self-assembly of three-dimensional microstructures
P. D'Acunto and J. J. C. Castellon Gonzalez -- Folding augmented: A design method to integrate structural folding in archietecture
S. Hoffmann, M. Barej, B. Gunther, M. Trautz, B. Corves, and J. Feldhusen -- Demands on an adapted design process for foldable structures
M. Ghosh, D. Tomkins, J. Denny, S. Rodriguez, M. Morales, and N. M. Amato -- Planning motions for shape-memory alloy sheets
N. Tsuruta, J. Mitani, Y. Kanamori, and Y. Fukui -- Simple flat origami exploration system with random folds
R. Chudoba, J. van der Woerd, and J. Hegger -- ORICREATE: Modeling framework for design and manufacturing of folded plate structures
Y. Miyamoto -- Rotation erection system (res): Origami extended with cuts
P. J. Mehner, T. Liu, A. B. Karimi, A. Brodeur, J. Paniagua, S. Giles, P. Richard, A. Nemtserova, S. Liu, R. C. Alperin, S. Bhatia, M. Culpepper, R. J. Lang, and C. Livermore -- Toward engineering biological tissues by directed assembly and origami folding
M. C. Neyrinck -- Cosmological origami: Properties of cosmic-web components when a non-stretchy dark-matter sheet folds
C. Cumino, E. Frigerio, S. Gallina, M. L. Spreafico, and U. Zich -- Modeling vaults in origami: A bridge between mathematics and architecture

Origami in art, design, and history

Y. Klett -- Folding perspectives: Joys and uses of 3d anomorhic origami
K. Box and R. J. Lang -- Master peace: An evolution of monumental origami
T. de Ruysser -- Wearable metal origami
J. Mosely -- Crowdsourcing origami sculptures
M. Gardiner -- On the aesthetics of folding and technology: Scale, dimensionality, and materiality
J. Maekawa -- Computational problems related to paper crane in the Edo period
H. Koshiro -- Mitate and origami

Origami in education

M. Golan and J. Oberman -- The kindergarten origametria programme
E. Frigerio and M. L. Spreafico -- Area and optimization problems
S.-P. Kwan -- Mathematics and art through the cubotahedron
A. Tubis -- Origami-inspired deductive threads in pre-geometry
H. Yanping and P.-Y. Lee -- Using paper folding to solve problems in school geometry
A. Bahmani, K. Sharif, and A. Hudson -- Using origami to enrich mathematical understanding of self similarity and fractals
L. Poladian -- Using the Fujimoto approximation technique to teach chaos theory to high school students