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Algebraic combinatorics has evolved into one of the most active
areas of mathematics. Its developments have become more interactive
with not only its traditional field representation theory but also
geometry, mathematical physics and harmonic analysis. This book
presents articles from some of the key contributors in the area. It
covers Hecke algebras, Hall algebras, the Macdonald polynomial and
its deviations, and their relations with other fields.

In presenting a detailed study of the geometry and topology of
numerous classes of "generic" singularities, Geometry of
Topological Stability bridges the gap between algebraic
calculations and continuity arguments to detail the necessary and
sufficient conditions for a C (infinity) to be C]0-stable.
Throughout, the authors masterfully examine this important subject
using results culled from a broad range of mathematical
disciplines, including geometric... more...

This book is a festschrift in honor of Professor Anthony Gaglione's
sixtieth birthday. This volume presents an excellent mix of
research and expository articles on various aspects of infinite
group theory. The papers give a broad overview of present research
in infinite group theory in general, and combinatorial group theory
and non-Abelian group-based cryptography in particular. They also
pinpoint the interactions between combinatorial group theory... more...

Mathematics is very much a part of our culture; and this invaluable
collection serves the purpose of developing the branches involved,
popularizing the existing theories and guiding our future
explorations. More precisely, the goal is to bring the reader to
the frontier of current developments in arithmetic geometry and
number theory through the works of Deninger-Werner in vector
bundles on curves over p-adic fields; of Jiang on local gamma
factors in... more...

This book develops model theory independently of any concrete
logical system or structure, within the abstract category-theoretic
framework of the so called ‘institution theory’. The development
includes most of the important methods and concepts of conventional
concrete model theory at the abstract institution-independent
level. Consequently it is easily applicable to a rather large
diverse collection of logics from the mathematical and computer... more...

This book is a collection of a series of lectures given by Prof. V
Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures
focus on the idea of a highest weight representation, which goes
through four different incarnationsThe first is the canonical
commutation relations of the infinite-dimensional Heisenberg
Algebra (= oscillator algebra). The second is the highest weight
representations of the Lie algebra gl? of infinite matrices, along... more...

Let G be a finite group and let F be a field. It is well known that
linear representations of G over F can be interpreted as modules
over the group algebra FG. Thus the investigation of ring-theoretic
structure of the Jacobson radical J(FG) of FG is of fundamental
importance. During the last two decades the subject has been
pursued by a number of researchers and many interesting results
have been obtained. This volume examines these results.
The main... more...

Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin
consists of invited expository and research articles on new
developments arising from Manin’s outstanding contributions to
mathematics.

This volume comprises the Lecture Notes of the CIMPA/TUBITAK Summer
School Arrangements, Local systems and Singularities held at
Galatasaray University, Istanbul during June 2007. The volume is
intended for a large audience in pure mathematics, including
researchers and graduate students working in algebraic geometry,
singularity theory, topology and related fields. The reader will
find a variety of open problems involving arrangements, local
systems... more...

The Art of Proof is designed for a one-semester or two-quarter
course. A typical student will have studied calculus (perhaps also
linear algebra) with reasonable success. With an artful mixture of
chatty style and interesting examples, the student's previous
intuitive knowledge is placed on solid intellectual ground. The
topics covered include: integers, induction, algorithms, real
numbers, rational numbers, modular arithmetic, limits, and
uncountable... more...