Series : Operator Theory: Advances and Applications , Vol. 156
2004, Approx. 312 p., Hardcover
ISBN: 3-7643-7145-5
About this book
Quadrature domains were singled out about 30 years ago by D.
Aharonov and H.S. Shapiro in connection with an extremal problem
in function theory. Since then, a series of coincidental
discoveries put this class of planar domains at the center of
crossroads of several quite independent mathematical theories, e.g.,
potential theory, Riemann surfaces, inverse problems, holomorphic
partial differential equations, fluid mechanics, operator theory.
The volume is devoted to recent advances in the theory of
quadrature domains, illustrating well the multi-facet aspects of
their nature. The book contains a large collection of open
problems pertaining to the general theme of quadrature domains
Table of contents
Preface.- Selected Bibliography of H.S. Shapiro.- Open Problems
Related to Quadrature Domains.- Contributions by A. Aleman, H.
Hedenmalm and S. Richter / S. Bell / J. Cima, A. Matheson and W.
Ross / D. Crowdy / P. Duren, A. Schuster and D. Vukotic / P.
Ebenfelt, D. Khavinson and H.S. Shapiro / B. Gustafsson and M.
Putinar / B. Gustafsson and H.S. Shapiro / M. Sakai / H.
Shahgholian / S. Shimorin / T. Sjodin / V. Tkatchev.
Series : Oberwolfach Seminars , Vol. 33 ←DMV Seminar よりシリーズ名変更（この巻より）
2004, XVI, 276 p., Softcover
ISBN: 3-7643-7141-2
Due: November 2004
About this textbook
These lecture notes contain a guided tour to the Novikov
Conjecture and related conjectures due to Baum-Connes, Borel and
Farrell-Jones. They begin with basics about higher signatures,
Whitehead torsion and the s-Cobordism Theorem. Then an
introduction to surgery theory and a version of the assembly map
is presented. Using the solution of the Novikov conjecture for
special groups some applications to the classification of low
dimensional manifolds are given. Finally, the most recent
developments concerning these conjectures are surveyed, including
a detailed status report. The prerequisites consist of a solid
knowledge of the basics about manifolds, vector bundles, (co-)
homology and characteristic classes.
Table of contents
Introduction.- A Motivating Problem.- Introduction to the Novikov
and Borel Conjecture.- Normal Bordism Groups.- The Signature.-
The Signature Theorem and the Novikov Conjecture.- The Projective
Class Group and the Whitehead Group.- Whitehead Torsion .- The
Statement and Consequences of the s-Cobordism Theorem.- Sketch of
the Proof of the s-Cobordism Theorem.- From the Novikov
Conjecture to Surgery.- Surgery Below the Middle Dimension I: An
Example.- Surgery Below the Middle Dimension II: Systematically
.- Surgery in the Middle Dimension I.- Surgery in the Middle
Dimension II.- Surgery in the Middle Dimension III.- An Assembly
Map.- The Novikov Conjecture for Z^.- Poincare Duality and
Algebraic L-Groups.- Spectra.- Classifying Spaces of Families.-
Equivariant Homology Theories and the Meta-Conjecture.- The
Farrell-Jones Conjecture.- The Baum-Connes Conjecture.- Relating
the Novikov, the Farrell-Jones and the Baum-Connes Conjectures.-
Miscellaneous.- Exercises.- Hints to the Solutions of the
Exercises.- References.- Index.- Notation.
2004, VIII, 336 p., Hardcover
ISBN: 3-7643-7158-7
Due: October 2004
About this book
The main objective of this book is to give a systematic
exposition of the main results and techniques of the
factorization theory of abelian groups. The necessary background
materials are presented along with some of the most important
applications in geometry, combinatorics, coding theory, and
number theory. A large part of the text is accessible to
students, requiring only basic knowledge in group theory and
algebra. Helpful exercises are provided in every chapter.
Researchers will find the book a comprehensive reference work on
the topic.
Table of contents
Preface.- 1. Hajos's and Redei's Theorems.- 2. Elementary
Arguments.- 3. The Machinery.- 4. Four Characterization Results.-
5. Applying the Machinery.- 6. Cyclic Prime Component.- 7. p-Groups.-
8. The Hajos Property.- 9. The Redei Property.- 10. Infinite
Groups.- 11. Further Topics.- Appendices.- References.- Index
Series : Frontiers in Mathematics
2005, Approx. 132 p., Hardcover
ISBN: 3-7643-7134-X
Due: January 2005
About this book
In this book we discuss invariant probabilities for a large class
of discrete-time homogeneous Markov processes known as Feller
processes. These Feller processes appear in the study of iterated
function systems with probabilities, convolution operators,
certain time series, etc. We obtain "formulas" for the
supports of various types of invariant probability measures, and
then we use these "formulas" to study properties of the
processes themselves. Rather than dealing with the processes, we
study the transition probabilities and the operators associated
to these processes. Although most of the results are new, the
book makes special efforts to attract newcomers to the theory of
Markov processes in general, and to the topics covered, in
particular.
Table of contents
Introduction.- Preliminaries on Markov-Feller Operators.- The
KBBY Decomposition.- Unique Ergodicity.- Equicontinuity.-
Bibliography.- Index.
300 pages
Hardback | available from February 2005
ISBN:0-521-83195-4
In 2002, an introductory workshop was held at the Mathematical
Sciences Research Institute in Berkeley to survey some of the
many new directions of the commutative algebra field. Six
principal speakers each gave three lectures, accompanied by a
help session, describing the interaction of commutative algebra
with other areas of mathematics for a broad audience of graduate
students and researchers. This book is based on those lectures,
together with papers from contributing researchers. David Benson
and Srikanth Iyengar present an introduction to the uses and
concepts of commutative algebra in the cohomology of groups. Mark
Haiman considers the commutative algebra of n points in the plane.
Ezra Miller presents an introduction to the Hilbert scheme of
points to complement Professor Haiman's paper. David Eisenbud and
Jessica Sidman give an introduction to the geometry of syzygies,
addressing the basic question of relating the geometry of a
projective variety with an embedding into projective space to the
minimal free resolution of its coordinate ring over the
polynomial ring of ambient projective space. Melvin Hochster
presents an introduction to the theory of tight closure. Graham
Leuschke adds a supporting paper on examples of tight closure and
how to compute it. Rob Lazarsfeld and Manuel Blickle discuss the
theory of multiplier ideals and how they can be used in
commutative algebra. Bernard Teissier presents ideas related to
resolution of singularities, complemented by Ana Bravo’s paper
on canonical subalgebra bases.
Contributors
David Benson, Mark Haiman, David Eisenbud, Melvin Hochster, Rob
Lazarsfeld, Bernard Teissier, Manuel Blickle, Ana Bravo, Srikanth
Iyengar, Graham Leuschke, Ezra Miller, Jessica Sidman
Publication is planned for May 2005
500 pages 43 line diagrams 2 tables 43 figures
Hardback | Not yet published - available from May 2005
ISBN:0521-84766-4
ISBN:052-161233-0(Paperback)
Probability and Statistics are as much about intuition and
problem solving, as they are about theorem proving. Because of
this, students can find it very difficult to make a successful
transition from lectures to examinations to practice, since the
problems involved can vary so much in nature. Since the subject
is critical in many modern applications such as mathematical
finance, quantitative management, telecommunications, signal
processing, bioinformatics, as well as traditional ones such as
insurance, social science and engineering, the authors have
rectified deficiencies in traditional lecture-based methods by
collecting together a wealth of exercises for which they have
supplied complete solutions. These solutions are adapted to needs
and skills of students. To make it of broad value, the authors
supply basic mathematical facts as and when they are needed, and
have sprinkled some historical information throughout the text.
Contents
Introduction; Part A. Probability: A1. Discrete outcomes; A2.
Continuous outcomes; A3. Index of problems for Part A; Part B.
Statistics: B1. Parameter estimation; B2. Hypothesis testing; B3.
Tripos exam questions in IB statistics (1992?2004); Tables of
random variables and probability distributions; Glossary.