Progress in Mathematics,Vol. 184
du Sautoy, M. / Segal, D. / Shalev,
A. (eds.):
This book presents a clear picture of the
rich universe of.pro-p groups in its unity
and diversity, with a systematic emphasis
on the construction and examination of many
classes of examples..A correspondingly diverse
range of mathematical techniques is successfully
applied, leading to new results and pointing
to.exciting new directions for research.
Connections with the.number of both local
and global fields are also explored. The
book includes the first complete account
in book form.of the theory of groups acting
on pro-p trees, of branch (Grigorchuk-type)
groups, and of the Nottingham group. The
book further includes a comprehensive survey
of Lie theoretic methods, and presents definitive
new results on the Glolod-Shafarevich condition
as well as a new treatment of cohomolgy of
p-adic analytic groups. The large number
of open research problems introduced and
discussed, and the excellent introductory
material and numerous examples presented
throughout, make this an indispe!
nsable reference text for researchers and
a suitable reference text for researchers
and a suitable text a one-semester graduate
course.
Apr. 2000 440 pp.
3-7643-4171-8 Birkhauer
This annual directory provides a handy reference
to various organizations in the mathematical
sciences community. Listed in the directory
are the following: officers and committee
members of over thirty professional mathematical
organizations (terms of office and other
pertinent information are also provided in
some cases); key mathematical sciences personnel
of selected government agencies; academic
departments in the mathematical sciences;
mathematical units in nonacademic organizations.
Mar. 2000 232 pp. 0-8218-2043-5
History of Mathematics, Series
Grassmann, H.:
The Ausdehnungslehre of 1862 is Grassmann's
most mature presentation of his "Extension
theory".
The work was unique in capturing the full
sweep of his mathemati-cal achievements.
Compared to Grassmann's first book, Lineale
Ausdehnungslehre, this book contains an enormous
amount of new material, including a detailed
development of the inner product and its
relation to the concept of angle, the "Theory
of functions" from the point of view
of extension theory, & Grassmann's contribution
to the Pfaff problem. In many ways, this
book is the version of Grassmann's system
most accessible to contemporary readers.
This translation is based on the material
in Grassmann's "Gesammelte Werke",
published by B. G. Teubner Mar.
2000 403 pp. 0-8218-2031-1
SMF/AMS Texts and Monographs, Vol. 3:
Bernadette Perrin-Riou, B. (eds.):
Traditionally, p-adic L-functions have been
constructed from complex L-functions via
special values and Iwasawa theory. In this
volume, Perrin-Riou presents a theory
of p-adic L-functions coming directly from
p-adic Galois representations.
This theory encompasses, in particular, a
construction of the module of p-adic L-functions
via the arithmetic theory and a conjectural
definition of the p-adic L-function via its
special values. Since the original publication
of this book in French (Asterisque 229)
Feb. 2000 150 pp. 0-8218-1946-1
Proceedings of Symposia in Applied Mathematics
Vol. 57:
Heath, D. / Swindle, G.(eds.):
The foundation for the subject of mathematical
finance was laid nearly 100 years ago by
Bachelier in his fundamental work, Theorie
de la speculation. In this work, he
provided the first treatment of Brownian
motion. Since then, the research of
Markowitz, and then of Black, Merton, Scholes,
and Samuelson brought remarkable and important
strides in the field. A few years later,
Harrison and Kreps demonstrated the fundamental
role of martingales and stochastic analysis
in constructing and understanding models
for financial markets.
Feb. 2000 172 pp. 0-8218-0751-X
The study of Diophantine equations has fascinated
mathematicians since antiquity.
Modern methods usedescribe the solutions
of Diophantine equations.
This introduction to the subject presents
complete proofs of four of the fundamental
finiteness theorems of Diophantine geometry.
Apr. 2000 520 pp. 0-387-98981-1
Reflection groups and invariant theory is
a branch of the intersect-ion between geometry
and algebra.
It has deep and elegant theory which is both
of greart interest in its own right and also
related to other significant areas of mathematics.
June 2000 320 pp. 0-387-98979-X
Springer
Mathemtical Sciences Research Institute Publications,
Vol. 39:
Haskell, D. / Pillay, A. / Steinhorn,C. (eds.):
Model theory (a branch of mathematical logic)
has, in recent years, made substantial contributions
to semialgebric, subanalytic, p-adic, rigid
and diophantine geometry. These applications
range from a proof of the rationality of
certain Poincare series associated to varieties
over p-adic fields, to a proof of the Mordell-Lang
conjecture for function fields in positive
characterstic. In some cases it is
the most abstract aspects of model theory
which are relevant. This book, arising
from a series of introductory lectures for
graduate students, provides the necessary
background to understanding both the model
theory and the mathematic behind these applications.
Apr. 2000 250 pp. 0-521-78068-3