Expected publication date is August 12, 2004
Description
The stationary tower is an important method in modern set theory,
invented by Hugh Woodin in the 1980s. It is a means of
constructing generic elementary embeddings and can be applied to
produce a variety of useful forcing effects.
Hugh Woodin is a leading figure in modern set theory, having made
many deep and lasting contributions to the field, in particular
to descriptive set theory and large cardinals. This book is the
first detailed treatment of his method of the stationary tower
that is generally accessible to graduate students in mathematical
logic. By giving complete proofs of all the main theorems and
discussing them in context, it is intended that the book will
become the standard reference on the stationary tower and its
applications to descriptive set theory.
The first two chapters are taken from a graduate course Woodin
taught at Berkeley. The concluding theorem in the course was that
large cardinals imply that all sets of reals in the smallest
model of set theory (without choice) containing the reals are
Lebesgue measurable. Additional sections include a proof (using
the stationary tower) of Woodin's theorem that, with large
cardinals, the Continuum Hypothesis settles all questions of the
same complexity as well as some of Woodin's applications of the
stationary tower to the studies of absoluteness and determinacy.
The book is suitable for a graduate course that assumes some
familiarity with forcing, constructibility, and ultrapowers. It
is also recommended for researchers interested in logic, set
theory, and forcing.
Contents
Elementary embeddings
The stationary tower
Applications
Forcing prerequisites
Bibliography
Index
Details:
Series: University Lecture Series, Volume: 32
Publication Year: 2004
ISBN: 0-8218-3604-8
Paging: approximately 144 pp.
Binding: Softcover
Expected publication date is August 7, 2004
Description
Supersymmetry has been studied by theoretical physicists since
the early 1970s. Nowadays, because of its novelty and
significance--in both mathematics and physics--the issues it
raises attract the interest of mathematicians.
Written by the well-known mathematician, V. S. Varadarajan, this
book presents a cogent and self-contained exposition of the
foundations of supersymmetry for the mathematically-minded reader.
It begins with a brief introduction to the physical foundations
of the theory, in particular, to the classification of
relativistic particles and their wave equations, such as those of
Dirac and Weyl. It then continues with the development of the
theory of supermanifolds, stressing the analogy with the
Grothendieck theory of schemes. Here, Varadarajan develops all
the super linear algebra needed for the book and establishes the
basic theorems: differential and integral calculus in
supermanifolds, Frobenius theorem, foundations of the theory of
super Lie groups, and so on. A special feature is the in-depth
treatment of the theory of spinors in all dimensions and
signatures, which is the basis of all supergeometry developments
in both physics and mathematics, especially in quantum field
theory and supergravity.
The material is suitable for graduate students and mathematicians
interested in the mathematical theory of supersymmetry. The book
is recommended for independent study.
Titles in this series are copublished with the Courant Institute
of Mathematical Sciences at New York University.
Contents
Introduction
The concept of a supermanifold
Super linear algebra
Elementary theory of supermanifolds
Clifford algebras, spin groups, and spin representations
Fine structure of spin modules
Superspacetimes and super Poincare groups
Details:
Series: Courant Lecture Notes, Volume: 11
Publication Year: 2004
ISBN: 0-8218-3574-2
Paging: 300 pp.
Binding: Softcover
Expected publication date is August 26, 2004
Description
This volume is based on talks given at the Workshop on
Categorical Structures for Descent and Galois Theory, Hopf
Algebras, and Semiabelian Categories held at The Fields Institute
for Research in Mathematical Sciences (Toronto, ON, Canada). The
meeting brought together researchers working in these
interrelated areas.
This collection of survey and research papers gives an up-to-date
account of the many current connections among Galois theories,
Hopf algebras, and semiabelian categories. The book features
articles by leading researchers on a wide range of themes,
specifically, abstract Galois theory, Hopf algebras, and
categorical structures, in particular quantum categories and
higher-dimensional structures.
Articles are suitable for graduate students and researchers,
specifically those interested in Galois theory and Hopf algebras
and their categorical unification.
Contents
M. Barr -- Algebraic cohomology: The early days
F. Borceux -- A survey of semi-abelian categories
D. Bourn -- Commutator theory in regular Mal'cev categories
D. Bourn and M. Gran -- Categorical aspects of modularity
R. Brown -- Crossed complexes and homotopy groupoids as non
commutative tools for higher dimensional local-to-global problems
M. Bunge -- Galois groupoids and covering morphisms in topos
theory
S. Caenepeel -- Galois corings from the descent theory point of
view
B. Day and R. Street -- Quantum categories, star autonomy, and
quantum groupoids
J. W. Duskin, R. W. Kieboom, and E. M. Vitale -- Morphisms of 2-groupoids
and low-dimensional cohomology of crossed modules
M. Gran -- Applications of categorical Galois theory in universal
algebra
C. Hermida -- Fibrations for abstract multicategories
J. Huebschmann -- Lie-Rinehart algebras, descent, and
quantization
P. Johnstone -- A note on the semiabelian variety of Heyting
semilattices
G. M. Kelly and S. Lack -- Monoidal functors generated by
adjunctions, with applications to transport of structure
M. Khalkhali and B. Rangipour -- On the cyclic homology of Hopf
crossed products
G. Lukacs -- On sequentially h-complete groups
J. L. MacDonald -- Embeddings of algebras
A. R. Magid -- Universal covers and category theory in polynomial
and differential Galois theory
N. Martins-Ferreira -- Weak categories in additive 2-categories
with kernels
T. Palm -- Dendrotopic sets
A. H. Roque -- On factorization systems and admissible Galois
structures
P. Schauenburg -- Hopf-Galois and bi-Galois extensions
J. D. H. Smith -- Extension theory in Mal'tsev varieties
L. Sousa -- On projective generators relative to coreflective
classes
J. J. Xarez -- The monotone-light factorization for categories
via preorders
J. J. Xarez -- Separable morphisms of categories via preordered
sets
S. Yamagami -- Frobenius algebras in tensor categories and
bimodule extensions
Details:
Series: Fields Institute Communications, Volume: 43
Publication Year: 2004
ISBN: 0-8218-3290-5
Paging: 570 pp.
Binding: Hardcover
Expected publication date is September 10, 2004
Description
Computational complexity theory is a major research area in
mathematics and computer science, the goal of which is to set the
formal mathematical foundations for efficient computation.
There has been significant development in the nature and scope of
the field in the last thirty years. It has evolved to encompass a
broad variety of computational tasks by a diverse set of
computational models, such as randomized, interactive,
distributed, and parallel computations. These models can include
many computers, which may behave cooperatively or adversarially.
Each summer the IAS/Park City Mathematics Institute Graduate
Summer School gathers some of the best researchers and educators
in the field to present diverse sets of lectures. This volume
presents three weeks of lectures given at the Summer School on
Computational Complexity Theory. Topics are structured as follows:
Week One: Complexity Theory: From Godel to Feynman. This section
of the book gives a general introduction to the field, with the
main set of lectures describing basic models, techniques,
results, and open problems.
Week Two: Lower Bounds on Concrete Models. Topics discussed in
this section include communication and circuit complexity,
arithmetic and algebraic complexity, and proof complexity.
Week Three: Randomness in Computation. Lectures are devoted to
different notions of pseudorandomness, interactive proof systems
and zero knowledge, and probabilistically checkable proofs (PCPs).
The volume is recommended for independent study and is suitable
for graduate students and researchers interested in computational
complexity.
Contents
Introduction
Week One. Complexity Theory: From Godel to Feynman: Steven
Rudich, Complexity Theory: From Godel to Feynman
Avi Wigderson, Average Case Complexity
Sanjeev Arora, Exploring Complexity through Reductions
Ran Raz, Quantum Computation
Week Two. Lower Bounds: Ran Raz, Circuit and Communication
Complexity
Paul Beame, Proof Complexity
Week Three. Randomness in Computation
Oded Goldreich, Pseudorandomness-Part I
Luca Trevisan, Pseudorandomness-Part II
Salil Vadhan, Probabilistic Proof Systems-Part I
Madhu Sudan, Probabilistically Checkable Proofs
Details:
Series: IAS/Park City Mathematics Series, Volume: 10
Publication Year: 2004
ISBN: 0-8218-2872-X
Paging: 389 pp.
Binding: Hardcover