Edited by:
Gopal Prasad, / Spencer Bloch / Igor Dolgachev / Ronald Fintushel /John Erik Forns
John Lott /G. A. Margulis / Andrew M. Odlyzko /Joel Smoller/ S.-T. Yau

A Special Volume of the Michigan Mathematical Journal in Honor of William Fulton

A publication of the University of Michigan, Department of Mathematics.

Description

This volume constitutes a special issue of the Michigan Mathematical Journal dedicated to William Fulton on the occasion of his sixtieth birthday. Attesting to the breadth of his contributions, the volume contains some thirty papers on a wide range of topics centered in algebraic geometry, representation theory, and
commutative algebra. This collection will be of interest to researchers and students in these and neighboring fields.

Contents

P. Aluffi and C. Faber -- Linear orbits of arbitrary plane curves
A. Beauville -- Determinantal hypersurfaces
A. Bertram -- Some applications of localization to enumerative problems
M. Brion -- Poincar・duality and equivariant (co)homology
H. Clemens and H. Kley -- On an example of Voisin
P. Deligne, M. Goresky, and R. MacPherson -- L'alg鐫re de cohomologie du compl駑ent dans un espace affine, d'une famille finie de sous-espaces affines
J.-P. Demailly, L. Ein, and R. Lazarsfeld -- A subadditivity property of multiplier ideals
P. Diaconis and A. Ram -- Analysis of systematic scan metropolis algorithms using Iwahori-Hecke algebra techniques
I. V. Dolgachev -- Polar cremona transformations
D. Edidin and W. Graham -- Good representations and solvable groups
C. Faber and R. Pandharipande -- Logarithmic series and Hodge integrals in the tautological ring
S. Fomin and M. Shapiro -- Stratified spaces formed by totally positive varieties
D. Franco, S. L. Kleiman, and A. T. Lascu -- Gherardelli linkage and complete intersections
T. Garrity -- Global structures on CR manifolds via Nash blow-ups
A. Givental -- On the WDVV-equation in quantum K-theory
M. Hochster and C. Huneke -- Localization and test exponents for tight closure
Y. Hu and S. Keel -- Mori dream spaces and GIT
T. J�zefiak -- A construction of irreducible $\mathrm{GL}(m)$-representatives
J. Koll疵 -- Fundamental groups of rationally connected varieties
A. Kresch -- Gromov-Witten invariants of a class of toric varieties
D. Laksov and A. Thorup -- The algebra of jets
A. Lascoux and P. Pragacz -- Orthogonal divided differences and Schubert polynomials, $\tilde{P}$-functions, and vertex operators
A. Losev and Y. Manin -- New modular spaces of pointed curves and pencils of flat connections
M. V. Nori -- The Hirzebruch-Riemann-Roch theorem
D. Perkinson -- Inflections of toric varieties
P. C. Roberts -- Intersection multiplicities and Hilbert polynomials
B. Shapiro, M. Shapiro, A. Vainshtein, and A. Zelevinsky -- Simply-laced Coxeter groups and groups generated by symplectic transvections
K. Smith -- Globally F-regular varieties: Applications to vanishing theorems for quotients of Fano varieties
F. Sottile -- Some real and unreal enumerative geometry for flag manifolds
H. Tamvakis -- Height formulas for homogeneous varieties
B. Totaro -- The topology of smooth divisors and the arithmetic of abelian varieties

Details:

Publisher: University of Michigan, Department of Mathematics
Distributor: American Mathematical Society
Publication Year: 2000
Paging: 600 pp.
Binding: Hardcover

Michael Mesterton-Gibbons, Florida State University, Tallahassee, FL

An Introduction to Game-Theoretic Modelling: Second Edition

From reviews for the First Edition:

"Readers will be hard-pressed to find a general introduction to game theory that blends biological and mathematical approaches more expertly. It is both a well-rounded survey and a reference work of lasting value."
-- Behavioral Ecology

"This book is an introduction to game theory with two specific features: it is written by a mathematician ... and it is written from the perspective of a mathematical modeller. This last characteristic implies that all chapters start with examples and the general concepts are only presented once the specific examples have been
carefully developed ... I find this book excellent and ... worth considering when teaching an undergraduate course in game theory to students having some mathematical maturity (some calculus, some knowledge of matrix analysis and probability)."
-- Zentralblatt fur Mathematik

Description

This book is about using game theory in mathematical modelling. It is an introductory text, covering the basic ideas and methods of game theory as well as the necessary ideas from the vast spectrum of scientific study where the methods are applied.

It has by now become generally apparent that game theory is a fascinating branch of mathematics with both serious and recreational applications. Strategic behavior arises whenever the outcome of an individual's action depends on actions to be taken by other individuals--whether human, as in the Prisoners' Dilemma, or
otherwise, as in the "duels of damselflies". As a result, game-theoretic mathematical models are applicable in both the social and natural sciences. In reading this book, you can learn not just about game theory, but also about how to model real situations so that they can be analyzed mathematically.

Mesterton-Gibbons includes the familiar game theory examples where they are needed for explaining the mathematics or when they provide a valuable application. There are also plenty of new examples, in particular from biology, such as competitions for territory or mates, games among kin versus games between kin, and
cooperative wildlife management.

Prerequisites are modest. Students should have some mathematical maturity and a familiarity with basic calculus, matrix algebra, probability, and some differential equations. As Mesterton-Gibbons writes, "The recurring theme is that game theory is fun to learn, doesnt require a large amount of mathematical rigor, and has great potential for application."

This new edition contains a significant amount of updates and new material, particularly on biological games. An important chapter on population games now has virtually all new material. The book is absolutely up-to-date with numerous references to the literature. Each chapter ends with a commentary which surveys current developments.

Contents

Noncooperative games
Evolutionary stability and other selection criteria
Cooperative games in strategic form
Characteristic function games
Cooperation and the prisoner's dilemma
More population games
Appraisal
The tracing procedure
Solutions to selected exercises
Bibliography
Index

Details:

Series: Student Mathematical Library, Volume: 11
Publication Year: 2000
ISBN: 0-8218-1929-1
Paging: 368 pp.
Binding: Softcover

Edited by:
Shui Feng,/Anna T. Lawniczak / S. R. S. Varadhan,

Hydrodynamic Limits and Related Topics

Description

This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in nongradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced
graduate course in hydrodynamic limits and interacting particle systems.

Contents
Part 1
S. R. S. Varadhan -- Lectures on hydrodynamic scaling

Part 2
J. A. Carrillo -- On a 1-d granular media immersed in a fluid
H. Fuks -- A class of cellular automata equivalent to deterministic particle systems
T. Funaki -- Recent results on the Ginzburg-Landau $\nabla\phi$ interface model
I. Grigorescu -- Large scale behavior of a system of interacting diffusions
R. Illner -- Stellar dynamics and plasma physics with corrected potentials: Vlasov, Manev, Boltzmann, Smoluchowski
J. Quastel -- Free boundary problem and hydrodynamic limit
T. Sepp舁臺nen -- A variational coupling for a totally asymmetric exclusion process with long jumps but no passing
H.-T. Yau -- Quantum mechanics, linear Boltzmann equation and renormalization

Details:

Series: Fields Institute Communications, Volume: 27
Publication Year: 2000
ISBN: 0-8218-1993-3
Paging: approximately 152 pp.
Binding: Hardcover

Javier Duoandikoetxea/Euskal Herriko

Fourier Analysis

Description

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calder�n and Zygmund. The text was born from a graduate course taught at the Universidad Aut�noma de Madrid and incorporates lecture notes from a course taught by Jos・Luis Rubio de Francia at the same university.

Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, $H^1$, $BMO$ spaces, and the $T1$ theorem, are discussed.

Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between $H^1$,
$BMO$, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the $T1$ theorem, which has been of crucial importance in the field.

This volume has been updated and translated from the Spanish edition that was published in 1995. Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references. It is geared toward
graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.

Contents

Fourier series and integrals
The Hardy-Littlewood maximal function
The Hilbert transform
Singular integrals (I)
Singular integrals (II)
$H^1$ and $BMO$
Weighted inequalities
Littlewood-Paley theory and multipliers
The $T1$ theorem
Bibliography

Details:

Series: Graduate Studies in Mathematics, Volume: 29
Publication Year: 2000
ISBN: 0-8218-2172-5
Paging: approximately 232 pp.
Binding: Hardcover

Edited by:
Ding-Zhu Du/ Panos M. Pardalos/Jie Wang

Discrete Mathematical Problems with Medical Applications

Description

This volume presents selected papers from a three-day workshop held during the DIMACS special years on Mathematical Support for Molecular Biology. Participants from the world over attended, giving the workshop an important international component.

The study of discrete mathematics and optimization with medical applications is emerging as an important new research area. Significant applications have been found in medical research, for example in radiosurgical treatment planning, virtual endoscopy, and more. This volume presents a substantive cross-section of active
research topics ranging from medical imaging to human anatomy modeling, from gamma knife treatment planning to radiation therapy, and from epileptic seizures to DNA screening. This book is an up-to-date resource reflecting current research directions.

Contents

Y.-J. Lee, O. L. Mangasarian, and W. H. Wolberg -- Breast cancer survival and chemotherapy: A support vector machine analysis
P. Hall -- A model for learning human vascular anatomy
M. C. Ferris and D. M. Shepard -- Optimization of gamma knife radiosurgery
Q. J. Wu -- Sphere packing using morphological analysis
L. D. Iasemidis, D.-S. Shiau, J. C. Sackellares, and P. Pardalos -- Transition to epileptic seizures: Optimization
I. Nystr�m and Smedby -- Analysis of magnetic resonance angiography images using skeletonization and distance transforms
S. Bouix and K. Siddiqi -- Computing medial surfaces
A. Rangarajan and H. Chui -- A mixed variable optimization approach to non-rigid image registration
B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp, and L. Zhang -- On computing the nearest neighbor interchange distance
A. J. Macula, D. C. Torney, and P. A. Vilenkin -- Two-stage group testing for complexes in the presence of errors
L. Sheng, C. Wang, and P. Zhang -- On the perfectness of tagged probe interval graphs
S. E. Brossette and A. P. Sprague -- Frequent sets in the presence of clones: An example from medical surveillance
H. Q. Ngo and D.-Z. Du -- A survey on combinatorial group testing algorithms with applications to DNA Library Screening
Q. J. Wu, C. H. Sibata, and J. Wang -- Optimization problems in 3D conformal radiation therapy
A. Kuba, G. T. Herman, S. Matej, and A. Todd-Pokropek -- Medical applications of discrete tomography
J. K. Udupa -- A study of 3D imaging approaches in medicine
P. Hall -- Discrete mathematics in medical imaging: A personal view

Details:

Series: DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume: 55
Publication Year: 2000
ISBN: 0-8218-2096-6
Paging: 248 pp.
Binding: Hardcover