Edited by: David Avis, McGill University, Montreal, QC, Canada, David Bremner, University of New Brunswick, Fredericton, NB, Canada, and Antoine Deza, McMaster University, Hamilton, ON, Canada

Polyhedral Computation

CRM Proceedings & Lecture Notes, Volume: 48
2009; 147 pp; softcover
ISBN-13: 978-0-8218-4633-9
Expected publication date is April 12, 2009.

Many polytopes of practical interest have enormous output complexity and are often highly degenerate, posing severe difficulties for known general-purpose algorithms. They are, however, highly structured, and attention has turned to exploiting this structure, particularly symmetry. Initial applications of this approach have permitted computations previously far out of reach, but much remains to be understood and validated experimentally.

The papers in this volume give a good snapshot of the ideas discussed at a Workshop on Polyhedral Computation held at the CRM in Montreal in October 2006 and, with one exception, the current state of affairs in this area. The exception is the inclusion of an often cited 1980 technical report of Norman Zadeh, which was never published in a journal and has passed into the folklore of the discipline. This paper illustrates beautifully the work still to be done in the field: it gives a simple pivot rule for the simplex method for which it is still unknown if it yields a polynomial time algorithm.

Readership

Graduate students and research mathematicians interested in discrete and computational geometry, combinatorial and continuous optimization, linear programming, enumeration algorithms, and computational complexity.

Table of Contents

Edited by: Tomasz S. Mrowka, Massachusetts Institute of Technology, Cambridge, MA, and Peter S. Ozsvath, Columbia University, New York, New York

Low Dimensional Topology

IAS/Park City Mathematics Series, Volume: 15
2009; 315 pp; hardcover
ISBN-13: 978-0-8218-4766-4
Expected publication date is May 16, 2009.

Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers.

The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.

Readership

Graduate students and research mathematicians interested in low dimensional topology.

Table of Contents

P. S. Ozsvath and T. S. Mrowka -- Introduction
J. Milnor -- Fifty years ago: Topology of manifolds in the 50's and 60's
C. Gordon -- Dehn surgery and 3-manifolds
D. Gabai -- Hyperbolic geometry and 3-manifold topology
J. W. Morgan -- Ricci flow and Thurston's geometrization conjecture (with notes by Max Lipyanskiy)
M. Asaeda and M. Khovanov -- Notes on link homology
Z. Szabo -- Lecture notes on Heegard Floer homology
J. Etnyre -- Contact geometry in low dimensional topology
R. Fintushel and R. J. Stern -- Six lectures on four 4-manifolds

Branko Grunbaum, University of Washington, Seattle, WA

Configurations of Points and Lines

Graduate Studies in Mathematics, Volume: 103
2009; approx. 480 pp; hardcover
ISBN-13: 978-0-8218-4308-6
Expected publication date is May 24, 2009.

This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers all the advances in the field since the revival of interest in geometric configurations some 20 years ago. The author's contributions are central to this revival. In particular, he initiated the study of 4-configurations (that is, those that contain four points on each line, and four lines through each point); the results are fully described in the text. The main novelty in the approach to all geometric configurations is the concentration on their symmetries, which make it possible to deal with configurations of rather large sizes. The book brings the readers to the limits of present knowledge in a leisurely way, enabling them to enjoy the material as well as entice them to try their hand at expanding it.

Readership

Undergraduate students, graduate students, and research mathematicians interested in an active field of visually accessible geometry and the applicability of computer graphics.

Table of Contents

Beginnings
3-Configurations
4-Configurations
Other configurations
Properties of configurations
Postscript
Appendix: The Euclidean, projective, and extended Euclidean planes
References

Edited by: Vyacheslav Futorny, Universidade de Sao Paulo, Brazil, Victor Kac, Massachusetts Institute of Technology, Cambridge, MA, Iryna Kashuba, Universidade de Sao Paulo, Brazil, and Efim Zelmanov, University of California, San Diego, La Jolla, CA

Algebras, Representations and Applications

Contemporary Mathematics, Volume: 483
2009; 285 pp; softcover
ISBN-13: 978-0-8218-4652-0
Expected publication date is May 9, 2009.

This volume contains contributions from the conference on "Algebras, Representations and Applications" (Maresias, Brazil, August 26-September 1, 2007), in honor of Ivan Shestakov's 60th birthday.

This book will be of interest to graduate students and researchers working in the theory of Lie and Jordan algebras and superalgebras and their representations, Hopf algebras, Poisson algebras, Quantum Groups, Group Rings and other topics.

Readership

Graduate students and research mathematicians interested in Lie and Jordan algebras and their representations.

Table of Contents

Edited by: Motoko Kotani, Tohoku University, Sendai, Japan, and Hisashi Naito and Tatsuya Tate, Nagoya University, Japan

Spectral Analysis in Geometry and Number Theory

Contemporary Mathematics, Volume: 484
2009; 342 pp; softcover
ISBN-13: 978-0-8218-4269-0
Expected publication date is May 10, 2009.

This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007.

Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.

Readership

Graduate students and research mathematicians interested in geometry, number theory, and dynamical systems.

Table of Contents