2010; 186 pp; hardcover
ISBN-13: 978-83-7326-798-5
Expected publication date is June 30, 2011.
This meticulously researched and detailed account of the life of the Polish mathematician Stefan Banach presents previously unknown facts that shed new light on his accomplishments and chronicles the many dramatic events of his life.
A self-taught prodigy and one of the great scientists of the twentieth century, Banach established modern functional analysis, an entirely new branch of mathematics with important applications. He also helped to develop the theory of topological vector spaces. Such notions as Banach space, Banach algebra, Banach manifold, Banach measure, Banach integral, Banach limit, and Banach bundle are widely used in today's mathematics.
The authors interviewed Banach's living family members, former students and acquaintances, unearthed old documents and records, and collected previously unpublished letters and photographs to compile this biography. They also added a concise overview of his pioneering work. Their research was motivated by a desire to provide an accurate and authoritative account of the life and achievements of one of Poland's most famous and celebrated mathematicians.
Readers interested in the history of Stefan Banach.
A remarkable life (by Emilia Jakimowicz)
Letters
Recollections
Stefan Banach in the light of archives (by Stanis?aw Domoradzki, Zofia Pawlikowska-Bro?ek, and Mikhailo Zarichny)
Banach's opus scientificus (by Julian Musielak)
Stefan Banach and Lvov Mathematical School (by Krzysztof Ciesielski and Zdzislaw Pogoda)
The Scottish Book (by Marek Kordos)
The New Scottish Book (by Roman Duda)
Selected bibliography in English and French
Selected bibliography in Polish
Biographical notes
List of illustrations
Index of names
AMS/IP Studies in Advanced Mathematics, Volume: 49
2011; 143 pp; softcover
ISBN-13: 978-0-8218-5352-8
Expected publication date is June 30, 2011.
This volume offers deep insight into the methods and concepts of a very active field of mathematics that has many connections with physics. Researchers and students will find it to be a useful source for their own investigations, as well as a general report on the latest topics of interest.
Presented are contributions from several specialists in differential geometry and mathematical physics, collectively demonstrating the wide range of applications of Lorentzian geometry, and ranging in character from research papers to surveys to the development of new ideas.
This volume consists mainly of papers drawn from the conference "New Developments in Lorentzian Geometry" (held in November 2009 in Berlin, Germany), which was organized with the help of the DFG Collaborative Research Center's "SFB 647 Space-Time-Matter" group, the Berlin Mathematical School, and Technische Universitat Berlin.
Graduate students and research mathematicians interested in Lorentzian geometry, special and general relativity.
R. Bartolo, A. M. Candela, and E. Caponio -- An Avez-Seifert type theorem for orthogonal geodesics on a stationary spacetime
M. Caballero and R. M. Rubio -- Calabi-Bernstein problems for spacelike slices in certain generalized Robertson-Walker spacetimes
Y. Choquet-Bruhat and J. M. Martin-Garcia -- A geometric energy estimate for data on a characteristic cone
R. Deszcz, M. G?ogowska, M. Hotlo?, and K. Sawicz -- A survey on generalized Einstein metric conditions
F. Dobarro and B. Unal -- Non-rotating killing vector fields on standard static space-times
R. Geroch -- Faster than light?
G. Hall -- Projective structure in space-times
P. G. LeFloch -- Einstein spacetimes with weak regularity
E. Minguzzi -- Time functions as utility functions
M. Sanchez -- Recent progress on the notion of global hyperbolicity
S. Suhr -- Homologically maximizing geodesics in conformally flat tori
MSRI Mathematical Circles Library, Volume: 4
2011; 220 pp; softcover
ISBN-13: 978-0-8218-5363-4
Expected publication date is July 13, 2011.
The Moscow Mathematical Olympiad has been challenging high-school students with stimulating, original problems of different degrees of difficulty for over 75 years. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation. Some are within the reach of most mathematically competent high-school students, while others are difficult even for a mathematics professor. Many mathematically inclined students have found that tackling these problems, or even just reading their solutions, is a great way to develop mathematical insight.
In 2006 the Moscow Center for Continuous Mathematical Education began publishing a collection of problems from the Moscow Mathematical Olympiads, providing for each an answer (and sometimes a hint) as well as one or more detailed solutions. This volume represents the years 1993-1999.
The problems and the accompanying material are well suited for math circles. They are also appropriate for problem-solving classes and practice for regional and national mathematics competitions.
High school and undergraduate students interested in problem solving; mathematical circles.
Problems
Answers
Hints
Solutions
Reference facts
Postscript by V. M. Tikhomirov: Reflections on the Moscow Mathematical Olympiads
Bibliography
Problem authorship
AMS/IP Studies in Advanced Mathematics,Volume: 50
2011; 446 pp; softcover
ISBN-13: 978-0-8218-5353-5
Expected publication date is July 23, 2011.
In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory.
The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
Graduate students and research mathematicians interested in mathematical physics; topological quantum field theory; Chern-Simons theory.
C. Beasley -- Remarks on Wilson loops and Seifert loops in Chern-Simons theory
T. Dimofte and S. Gukov -- Quantum field theory and the volume conjecture
J. Dubois -- Computational aspects in Reidemeister torsion and Chern-Simons theories
E. Guadagnini -- Functional integration and abelian link invariants
M. Hedden and P. Kirk -- Chern-Simons invariants, SO(3) instantons, and mathbb{Z}/2 homology cobordism
C. M. Herald -- Extending the SU(3) Casson invariant to rational homology 3-spheres
K. Hikami -- Decomposition of Witten-Reshetikhin-Turaev invariant: Linking pairing and modular forms
K. Hikami and H. Murakami -- Representations and the colored Jones polynomial of a torus knot
L. Jeffrey and B. McLellan -- Eta-invariants and anomalies in U/1 Chern-Simons theory
R. M. Kashaev -- Delta-groupoids and ideal triangulations
C. Lescop -- Invariants of knots and 3-manifolds derived from the equivariant linking pairing
M. Marino -- Chern-Simons theory, the 1/N expansion, and string theory
C. Meusburger -- Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)-gravity see?
A. Mikovi? and J. F. Martins -- Spin foam state sums and Chern-Simons theory
R. C. Penner -- Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants
A. N. Sengupta -- Yang-Mills in two dimensions and Chern-Simons in three
G. Thompson -- Intersection pairings on spaces of connections and Chern-Simons theory on Seifert manifolds
J. Weitsman -- Fermionization and convergent perturbation expansions in Chern-Simons gauge theory
E. Witten -- Analytic continuation of Chern-Simons theory
CBMS Regional Conference Series in Mathematics, Number: 115
2011; 96 pp; softcover
ISBN-13: 978-0-8218-5315-3
Expected publication date is July 23, 2011.
Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph.
This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.
Graduate students and research mathematicians interested in graph theory.
Some fundamentals
Eigenvalues of graphs
Rado-Hall theorem and applications
Colin de Verdiere number
Classes of matrices of zeros and ones
Matrix sign patterns
Eigenvalue Inclusion and Diagonal Products
Tournaments
Two matrix polytopes
Digraphs and eigenvalues of (0,1)-matrices
Index
Mathematical Surveys and Monographs, Volume: 175
2011; approx. 297 pp; hardcover
ISBN-13: 978-0-8218-4496-0
Expected publication date is July 27, 2011.
Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.
Graduate students and research mathematicians interested in algebra or design theory.
Overview
Many kinds of pairwise combinatorial designs
A primer for algebraic design theory
Orthogonality
Modeling Lambda-equivalence
The Grammian
Transposability
New designs from old
Automorphism groups
Group development and regular actions on arrays
Origins of cocyclic development
Group extensions and cocycles
Cocyclic pairwise combinatorial designs
Centrally regular actions
Cocyclic associates
Special classes of cocyclic designs
The Paley matrices
A large family of cocyclic Hadamard matrices
Substitution schemes for cocyclic Hadamard matrices
Calculating cocyclic development rules
Cocyclic Hadamard matrices indexed by elementary abelian groups
Cocyclic concordant systems of orthogonal designs
Asymptotic existence of cocyclic Hadamard matrices
Bibliography
Index