Expected publication date is April 13, 2006
Description
This classic book is based on lectures given by the author at the
University of Chicago in 1956. The topics covered include, in
particular, recurrence, the ergodic theorems, and a general
discussion of ergodicity and mixing properties. There is also a
general discussion of the relation between conjugacy and
equivalence. With minimal prerequisites of some analysis and
measure theory, this work can be used for a one-semester course
in ergodic theory or for self-study.
Contents
Introduction
Examples
Recurrence
Mean convergence
Pointwise convergence
Comments on the ergodic theorem
Ergodicity
Consequences of ergodicity
Mixing
Measure algebras
Discrete spectrum
Automorphisms of compact groups
Generalized proper values
Weak topology
Weak approximation
Uniform topology
Uniform approximation
Category
Invariant measures
Invariant measures: the solution
Invariant measures: the problem
Generalized ergodic theorems
Unsolved problems
References
Details:
Series: AMS Chelsea Publishing
Publication Year: 1956
ISBN: 0-8218-4125-4
Paging: 99 pp.
Binding: Hardcover
Expected publication date is April 15, 2006
Description
Most of the papers in this book deal with the theory of Riemann
surfaces (moduli problems, automorphisms, etc.), abelian
varieties, theta functions, and modular forms. Some of the papers
contain surveys on the recent results in the topics of current
interest to mathematicians, whereas others contain new research
results.
Readership
Graduate students and research mathematicians interested in
algebraic geometry and complex geometry.
Contents
A. Basmajian and M. Zeinalian -- Mobius transformations of the
circle form a maximal convergence group
A. Campillo and J. Olivares -- On the polar linear system of a
foliation by curves in a projective space
F. J. Cirre -- Birational classification of hyperelliptic real
algebraic curves
C. J. Earle -- The genus two Jacobians that are isomorphic to a
product of elliptic curves
H. M. Farkas -- Vanishing thetanulls and Jacobians
C. Florentino, J. Mourao, and J. P. Nunes -- Theta functions,
geometric quantization and unitary Schottky bundles
Y. Fuertes and G. Gonzalez-Diez -- Smooth double coverings of
hyperelliptic curves
J. Gilman and L. Keen -- Planar families of discrete groups
E. Gomez Gonzalez and C. Gonzalez-Martinez -- Generalized
addition formulae for theta functions
E. Gomez Gonzalez and F. J. P. Martin -- Curves with a group
action and Galois covers via infinite Grassmannians
V. Gonzalez-Aguilera, J. M. Munoz-Porras, and A. G. Zamora --
Some recent results on the irreducible components of the singular
locus of A_g
M. R. Gonzalez-Dorrego -- A note on the arithmetic genus of
reducible plane curves
F. Herrlich -- Teichmuller curves defined by characteristic
origamis
H. A. Hidalgo and B. Maskit -- Lowest uniformizations of compact
real surfaces
H. Lange -- Principal polarizations on products of elliptic
curves
F. P. Romo -- An approach to a 2-dimensional Contou-Carrere
symbol
S. Recillas and R. E. Rodriguez -- Prym varieties and fourfold
covers II: The dihedral case
G. Schmithusen -- Examples for Veech groups of origamis
R. Silhol -- Genus 2 translation surfaces with an order 4
automorphism
R. Smith and R. Varley -- The Pfaffian structure defining a Prym
theta divisor
Details:
Series: Contemporary Mathematics, Volume: 397
Publication Year: 2006
ISBN: 0-8218-3855-5
Paging: 236 pp.
Binding: Softcover
Expected publication date is April 16, 2006
Description
The aim of this volume is to bring together research ideas from
various fields of mathematics which utilize the heat kernel or
heat kernel techniques in their research. The intention of this
collection of papers is to broaden productive communication
across mathematical sub-disciplines and to provide a vehicle
which would allow experts in one field to initiate research with
individuals in another field, as well as to give non-experts a
resource which can facilitate expanding their research and
connecting with others.
Readership
Graduate students and research mathematicians interested in
analysis, representation theory, algebraic geometry, partial
differential equations, mathematical physics.
Contents
L. Barchini, M. Sepanski, and R. Zierau -- Positivity of zeta
distributions and small unitary representations
R. Berndt -- The heat equation and representations of the Jacobi
group
J. Dodziuk and V. Mathai -- Kato's inequality and asymptotic
spectral properties for discrete magnetic Laplacians
D. S. Fine -- The heat kernel in low-dimensional quantum theories
A. Grigor'yan -- Heat kernels on weighted manifolds and
applications
J. F. Grotowski -- Heat kernels in geometric evolution equations
B. C. Hall -- The range of the heat operator
B. Harris -- Heat kernels and cycles
G. Hein -- Green currents on Kahler manifolds
S. Hofmann -- Heat kernels and Riesz transforms
M. D. Horton, D. B. Newland, and A. A. Terras -- The contest
between the kernels in the Selberg trace formula for the (q+1)-regular
tree
J. Jorgenson and J. Kramer -- Expressing Arakelov invariants
using hyperbolic heat kernels
M. H. Lee and E. Previato -- Grassmannians of higher local fields
and multivariable tau functions
V. Mathai and I. Chatterji -- Heat kernels and the range of the
trace on completions of twisted group algebras
E. Previato -- Theta functions, old and new
P. Sawyer -- The heat kernel on the symmetric space mathbf{SL}(n,mathbf{F})/mathbf{SU}(n,mathbf{F})
B. Wang -- Incidence structure
Details:
Series: Contemporary Mathematics, Volume: 398
Publication Year: 2006
ISBN: 0-8218-3698-6
Paging: 402 pp.
Binding: Softcover
Expected publication date is May 31, 2006
Description
Euler is one of the greatest and most prolific mathematicians of
all time. He wrote the first accessible books on calculus,
created the theory of circular functions, and discovered new
areas of research such as elliptic integrals, the calculus of
variations, graph theory, divergent series, and so on. It took
hundreds of years for his successors to develop in full the
theories he began, and some of his themes are still at the center
of today's mathematics. It is of great interest therefore to
examine his work and its relation to current mathematics. This
book attempts to do that.
In number theory the discoveries he made empirically would
require for their eventual understanding such sophisticated
developments as the reciprocity laws and class field theory. His
pioneering work on elliptic integrals is the precursor of the
modern theory of abelian functions and abelian integrals. His
evaluation of zeta and multizeta values is not only a fantastic
and exciting story but very relevant to us, because they are at
the confluence of much research in algebraic geometry and number
theory today (Chapters 2 and 3 of the book).
Anticipating his successors by more than a century, Euler created
a theory of summation of series that do not converge in the
traditional manner. Chapter 5 of the book treats the progression
of ideas regarding divergent series from Euler to many parts of
modern analysis and quantum physics.
The last chapter contains a brief treatment of Euler products.
Euler discovered the product formula over the primes for the zeta
function as well as for a small number of what are now called
Dirichlet L-functions. Here the book goes into the development of
the theory of such Euler products and the role they play in
number theory, thus offering the reader a glimpse of current
developments (the Langlands program).
Readership
Undergraduates, graduate students, and research mathematicians
interested in the history of mathematics and Euler's influence on
modern mathematics.
Contents
Leonhard Euler (1707-1783)
The universal mathematician
Zeta values
Euler-Maclaurin sum formula
Divergent series and integrals
Euler products
Gallery
Details:
Publication Year: 2006
ISBN: 0-8218-3580-7
Paging: 296 pp.
Binding: Hardcover
Expected publication date is May 24, 2006
Description
This book is an expanded text for a graduate course in
commutative algebra, focusing on the algebraic underpinnings of
algebraic geometry and of number theory. Accordingly, the theory
of affine algebras is featured, treated both directly and via the
theory of Noetherian and Artinian modules, and the theory of
graded algebras is included to provide the foundation for
projective varieties. Major topics include the theory of modules
over a principal ideal domain, and its applications to matrix
theory (including the Jordan decomposition), the Galois theory of
field extensions, transcendence degree, the prime spectrum of an
algebra, localization, and the classical theory of Noetherian and
Artinian rings. Later chapters include some algebraic theory of
elliptic curves (featuring the Mordell-Weil theorem) and
valuation theory, including local fields.
One feature of the book is an extension of the text through a
series of appendices. This permits the inclusion of more advanced
material, such as transcendental field extensions, the
discriminant and resultant, the theory of Dedekind domains, and
basic theorems of rings of algebraic integers. An extended
appendix on derivations includes the Jacobian conjecture and
Makar-Limanov's theory of locally nilpotent derivations. Grobner
bases can be found in another appendix.
Exercises provide a further extension of the text. The book can
be used both as a textbook and as a reference source.
Readership
Graduate students interested in algebra, geometry, and number
theory. Research mathematicians interested in algebra.
Contents
Part 0. Introduction
Part 0. Introduction
Introduction and prerequisites
Exercises-Part 0
Part I. Modules
Introduction to modules and their structure theory
Finiteley generated modules
Simple modules and composition series
Exercises-Part I
Part II. Affine algebras and Noetherian rings
Part II introduction
Galois theory of fields
Algebras and affine fields
Transcendence degree and the Krull dimension of a ring
Modules and rings satisfying chain conditions
Localization and the prime spectrum
The Krull dimension theory of commutative Noetherian rings
Exercises-Part II
Part III. Applications to geometry and number theory
Part III. Introduction
The algebraic foundations of geometry
Applications to algebraic geometry over the rationals --
Diophantine equations and elliptic curves
Absolute values and valuation rings
Exercises-Part III
References
Index
Details:
Series: Graduate Studies in Mathematics, Volume: 73
Publication Year: 2006
ISBN: 0-8218-0570-3
Paging: approx. 399 pp.
Binding: Hardcover