Description
The Workshop on Real and Complex Singularities is held every
other year at the Instituto de Ciencias Matematicas e de
Computacao (Sao Carlos, Brazil) and brings together specialists
in the vanguard of singularities and its applications. This
volume contains articles contributed by participants of the
seventh workshop.
The included papers reflect Fields Medalist Rene Thom's original
vision of singularities and represent all branches of the subject:
equisingularity of sets and mappings, the geometry of singular
complex analytic sets, singularities of mappings and their
elimination, characteristic classes, applications to differential
geometry, differential equations, and bifurcation theory.
The book is suitable for graduate students and researchers
interested in singularity theory.
Contents
J. W. Bruce, G. J. Fletcher, and F. Tari -- Zero curves of
families of curve congruences
A. Dimca and A. Nemethi -- Hypersurface complements, Alexander
modules and monodromy
D. Dreibelbis -- Invariance of the diagonal contribution in a
bitangency formula
E. Esteves and S. L. Kleiman -- Bounds on leaves of foliations of
the plane
L. Feher and R. Rimanyi -- Calculation of Thom polynomials and
other cohomological obstructions for group actions
A. C. G. Fernandes and C. H. Soares, Jr. -- On the bilipschitz
triviality of families of real maps
J.-E. Furter and A. M. Sitta -- A note on the path formulation
for (mathbb{O}(2),mathbb{SO}(2))-forced symmetry breaking
bifurcation
T. Gaffney -- Polar methods, invariants of pairs of modules and
equisingularity
I. S. Labouriau and C. M. S. G. Rito -- Stability of equilibria
in equations of Hodgkin-Huxley type
A. Libgober -- Isolated non-normal crossings
A. Nemethi -- Invariants of normal surface singularities
R. D. S. Oliveira -- Families of pairs of Hamiltonian vector
fields in the plane
A. A. du Plessis and C. T. C. Wall -- Topology of unfoldings of
singularities in the E, Z and Q series
M. C. Romero-Fuster -- Semiumbilics and geometrical dynamics on
surfaces in 4-spaces
D. Siersma and M. Tibar -- On the vanishing cycles of a
meromorphic function on the complement of its poles
J. Stevens -- Some adjacencies to cusp singularities
A. Szucs -- Elimination of singularities by cobordism
Details:
Series: Contemporary Mathematics, Volume: 354
Publication Year: 2004
ISBN: 0-8218-3665-X
Paging: 324 pp.
Binding: Softcover
Description
Knots are familiar objects. We use them to moor our boats, to
wrap our packages, to tie our shoes. Yet the mathematical theory
of knots quickly leads to deep results in topology and geometry.
The Knot Book is an introduction to this rich theory, starting
with our familiar understanding of knots and a bit of college
algebra and finishing with exciting topics of current research.
The Knot Book is also about the excitement of doing mathematics.
Colin Adams engages the reader with fascinating examples, superb
figures, and thought-provoking ideas. He also presents the
remarkable applications of knot theory to modern chemistry,
biology, and physics.
This is a compelling book that will comfortably escort you into
the marvelous world of knot theory. Whether you are a mathematics
student, someone working in a related field, or an amateur
mathematician, you will find much of interest in The Knot Book.
Colin Adams received the Mathematical Association of America (MAA)
Award for Distinguished Teaching and has been an MAA Polya
Lecturer and a Sigma Xi Distinguished Lecturer.
Contents
Introduction
Tabulating knots
Invariants of knots
Surfaces and knots
Types of knots
Polynomials
Biology, chemistry, and physics
Knots, links, and graphs
Topology
Higher dimensional knotting
Knot jokes and pastimes
Appendix
Suggested readings and references
Index
Corrections to the 2004 AMS printing
Details:
Publication Year: 2004
ISBN: 0-8218-3678-1
Paging: 307 pp.
Binding: Softcover
Description
Around 1980, G. Mason announced the classification of a certain
subclass of an important class of finite simple groups known as
"quasithin groups". The classification of the finite
simple groups depends upon a proof that there are no unexpected
groups in this subclass. Unfortunately Mason neither completed
nor published his work. In the Main Theorem of this two-part book
(Volumes 111 and 112 in the AMS series, Mathematical Surveys and
Monographs) the authors provide a proof of a stronger theorem
classifying a larger class of groups, which is independent of
Mason's arguments. In particular, this allows the authors to
close this last remaining gap in the proof of the classification
of all finite simple groups.
An important corollary of the Main Theorem provides a bridge to
the program of Gorenstein, Lyons, and Solomon (Volume 40 in the
AMS series, Mathematical Surveys and Monographs) which seeks to
give a new, simplified proof of the classification of the finite
simple groups.
Part I (the current volume) contains results which are used in
the proof of the Main Theorem. Some of the results are known and
fairly general, but their proofs are scattered throughout the
literature; others are more specialized and are proved here for
the first time.
Part II of the work (Volume 112) contains the proof of the Main
Theorem, and the proof of the corollary classifying quasithin
groups of even type.
The book is suitable for graduate students and researchers
interested in the theory of finite groups.
Contents
Volume I: Structure of strongly quasithin mathcal{K}-groups
Introduction to volume I
Elementary group theory and the known quasithin groups
Basic results related to failure of factorization
Pushing-up in SQTK-groups
The qrc-lemma and modules with hat{q}leq 2
Generation and weak closure
Weak BN-pairs and amalgams
Various representation-theoretic lemmas
Parameters for some modules
Statements of some quoted results
A characterization of the Rudvalis group
Modules for SQTK-groups with hat{q}(G, V) leq 2
Bibliography and index
Background references quoted (Part 1: also used by GLS)
Background references quoted (Part 2: used by us but not by GLS)
Expository references mentioned
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 111
Publication Year: 2004
ISBN: 0-8218-3410-X
Paging: approximately 496 pp.
Binding: Hardcover
Description
Around 1980, G. Mason announced the classification of a certain
subclass of an important class of finite simple groups known as
"quasithin groups". The classification of the finite
simple groups depends upon a proof that there are no unexpected
groups in this subclass. Unfortunately Mason neither completed
nor published his work. In the Main Theorem of this two-part book
(Volumes 111 and 112 in the AMS series, Mathematical Surveys and
Monographs) the authors provide a proof of a stronger theorem
classifying a larger class of groups, which is independent of
Mason's arguments. In particular, this allows the authors to
close this last remaining gap in the proof of the classification
of all finite simple groups.
An important corollary of the Main Theorem provides a bridge to
the program of Gorenstein, Lyons, and Solomon (Volume 40 in the
AMS series, Mathematical Surveys and Monographs) which seeks to
give a new, simplified proof of the classification of the finite
simple groups.
Part I (Volume 111) contains results which are used in the proof
of the Main Theorem. Some of the results are known and fairly
general, but their proofs are scattered throughout the
literature; others are more specialized and are proved here for
the first time.
Part II of the work (the current volume) contains the proof of
the Main Theorem, and the proof of the corollary classifying
quasithin groups of even type.
The book is suitable for graduate students and researchers
interested in the theory of finite groups.
Contents
Volume II: Main theorems; the classification of simple QTKE-groups
Introduction to volume II
Structure of QTKE-groups and the main case division
Structure and intersection properties of 2-locals
Classifying the groups with |mathcal{M}(T)|=1
Determining the cases for L in mathcal{L}^*_f(GT)
Pushing up in QTKE-groups
The treatment of the generic case
The generic case: L_2(2^n) in mathcal{L}_f and n(H)>1
Reducing L_2(2^n) to n=2 and V orthogonal
Modules which are not FF-modules
Eliminating cases corresponding to no shadow
Eliminating shadows and characterizing the J_4 example
Eliminating Omega^+_4(2^n) on its orthogonal module
Pairs in the FSU over F_{2^n} for n>1
The case L in mathcal{L}^*_f(G,T) not normal in M
Elimination of L_3(2^n), Sp_4(2^n), and G_2(2^n) for n>1
Groups over F_2
Larger groups over F_2 in mathcal{L}^*_f(G,T)
Mid-size groups over F_2
L_3(2) in the FSU, and L_2(2) when mathcal{L}_f(G,T) is empty
The case mathcal{L}_f(G,T) empty
The case mathcal{L}_f(G,T)=emptyset
The even type theorem
Quasithin groups of even type but not even characteristic
Bibliography and index
Background references quoted (Part 1: also used by GLS)
Background references quoted (Part 2: used by us but not by GLS)
Expository references mentioned
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 112
Publication Year: 2004
ISBN: 0-8218-3411-8
Paging: approximately 800 pp.
Binding: Hardcover
Description
This volume grew out of two ergodic theory workshops held at the
University of North Carolina at Chapel Hill. These events gave
young researchers an introduction to active research areas and
promoted interaction between young and established mathematicians.
Included are research and survey articles devoted to various
topics in ergodic theory. The book is suitable for graduate
students and researchers interested in these and related areas.
Contents
E. Akin -- Why is the 3x+1 problem hard?
E. Akin -- Lectures on Cantor and Mycielski sets for dynamical
systems
I. Assani -- Duality and the one-sided ergodic Hilbert transform
J. Auslander and K. Berg -- Rigidity conditions in topological
dynamics related to a theorem of George Sell
G. Cohen, R. L. Jones, and M. Lin -- On strong laws of large
numbers with rates
C. Demeter and R. L. Jones -- Besicovitch weights and the
necessity of duality restrictions in the weighted ergodic theorem
R. L. Jones -- Strong sweeping out for lacunary sequences
I. Kornfeld -- Some old and new Rokhlin towers
Details:
Series: Contemporary Mathematics, Volume: 356
Publication Year: 2004
ISBN: 0-8218-3313-8
Paging: 169 pp.
Binding: Softcover
Description
This volume contains the proceedings of the conference on
Variational Methods: Open Problems, Recent Progress, and
Numerical Algorithms. It presents current research in variational
methods as applied to nonlinear elliptic PDE, although several
articles concern nonlinear PDE that are nonvariational and/or
nonelliptic. The book contains both survey and research papers
discussing important open questions and offering suggestions on
analytical and numerical techniques for solving those open
problems.
It is suitable for graduate students and research mathematicians
interested in elliptic partial differential equations.
Contents
A. Castro -- Semilinear equations with discrete spectrum
G. Chen, Y. Deng, W.-M. Ni, and J. Zhou -- Semilinear elliptic
boundary value problems with nonlinear oblique boundary
conditions, a boundary element monotone iteration approach
G. Chen, Z. Ding, C.-R. Hu, W.-M. Ni, and J. Zhou -- A note on
the elliptic Sine-Gordon equation
G. Chen, B. G. Englert, and J. Zhou -- Convergence analysis of an
optimal scaling algorithm for semilinear elliptic boundary value
problems
J. W. Neuberger and R. J. Renka -- Sobolev gradients:
Introduction, applications, problems
D. G. Costa and H. Tehrani -- Unbounded perturbations of resonant
Schrodinger equations
J. Cepicka, P. Drabek, and P. Girg -- Quasilinear boundary value
problems: Existence and multiplicity results
P. Drabek and S. B. Robinson -- Eigenvalue problems, resonance
problems and open problems
P. Padilla -- Variational, dynamic and geometric aspects of some
nonlinear problems
V. L. Shapiro -- The perturbed p-Laplacian and quadratic growth
I. Knowles -- Variational methods for ill-posed problems
J. M. Neuberger -- GNGA: Recent progress and open problems for
semilinear elliptic PDE
F. Catrina -- Critical nonlinearities and symmetric solutions
J. A. Iaia -- Non-convergent radial solutions of a semilinear
elliptic equation in mathbb{R}^N
Z. Feng -- Traveling wave solutions to nonlinear evolution
equations
Details:
Series: Contemporary Mathematics,Volume: 357
Publication Year: 2004
ISBN: 0-8218-3339-1
Paging: 285 pp.
Binding: Softcover