Expected publication date is November 10, 2002
Description
This book is a collection of papers given by invited speakers at
the first AMS Special Session on Quantum Computation and
Information held at the January 2000 Annual Meeting of the AMS in
Washington, DC.
The papers in this volume give readers a broad introduction to
the many mathematical research challenges posed by the new and
emerging field of quantum computation and quantum information. Of
particular interest is a long paper by Lomonaco and Kauffman
discussing mathematical and computational aspects of the so-called
hidden subgroup algorithm.
This book is intended to help readers recognize that, as a result
of this new field of quantum information science, mathematical
research opportunities abound in such diverse mathematical fields
as algebraic coding theory, algebraic geometry, algebraic
topology, communication theory, control theory, cryptography,
differential geometry, differential topology, dynamical systems,
game theory, group theory, information theory, number theory,
operator theory, robotics, theory of computation, mathematical
logic, mathematical physics, and more. It is hoped that this book
will act as a catalyst to encourage members of the mathematical
community to take advantage of the many mathematical research
opportunities arising from the "grand challenge" of
Quantum Information Science.
This book is the companion volume to Quantum Computation: A Grand
Mathematical Challenge for the Twenty-First Century and the
Millennium, Volume 58 in the Proceedings of Symposia in Applied
Mathematics series.
Contents
P. Benioff -- Space searches with a quantum
robot
G. P. Berman, G. D. Doolen, D. I. Kamenev,
G. V. Lopez, and V. I. Tsifrinovich -- Perturbation
theory and numerical modeling of quantum
logic operations with a large number of qubits
H. E. Brandt -- Inconclusive rate with a
positive operator valued measure
G. Brassard, P. Hoyer, M. Mosca, and A. Tapp
-- Quantum amplitude amplification and estimation
L. Hardy -- Manipulating the entanglement
of one copy of a two-particle pure entangled
state
T. F. Havel and C. J. L. Doran -- Geometric
algebra in quantum information processing
L. H. Kauffman -- Quantum computing and the
Jones polynomial
S. J. Lomonaco, Jr. and L. H. Kauffman --
Quantum hidden subgroup algorithms: A mathematical
perspective
E. N. Maneva and J. A. Smolin -- Improved
two-party and multi-party purification protocols
D. A. Meyer -- Quantum games and quantum
algorithms
J. M. Myers and F. H. Madjid -- A proof that
measured data and equations of quantum mechanics
can be linked only by guesswork
J. Pachos -- Quantum computation by geometrical
means
M. B. Ruskai -- Pauli exchange and quantum
error correction
B. Schumacher and M. D. Westmoreland -- Relative
entropy in quantum information theory
N. R. Wallach -- An unentangled Gleason's
theorem
W. K. Wootters -- Entangled chains
Details:
Series: Contemporary Mathematics, Volume:
305
Publication Year: 2002
ISBN: 0-8218-2140-7
Paging: 310 pp.
Binding: Softcover
Expected publication date is November 14, 2002
Description
Ideas and techniques from the theory of integrable systems are
playing an increasingly important role in geometry. Thanks to the
development of tools from Lie theory, algebraic geometry,
symplectic geometry, and topology, classical problems are
investigated more systematically. New problems are also arising
in mathematical physics. A major international conference was
held at the University of Tokyo in July 2000. It brought together
scientists in all of the areas influenced by integrable systems.
This book is the first of three collections of expository and
research articles.
This volume focuses on differential geometry. It is remarkable
that many classical objects in surface theory and submanifold
theory are described as integrable systems. Having such a
description generally reveals previously unnoticed symmetries and
can lead to surprisingly explicit solutions. Surfaces of constant
curvature in Euclidean space, harmonic maps from surfaces to
symmetric spaces, and analogous structures on higher-dimensional
manifolds are some of the examples that have broadened the
horizons of differential geometry, bringing a rich supply of
concrete examples into the theory of integrable systems.
Many of the articles in this volume are written by prominent
researchers and will serve as introductions to the topics. It is
intended for graduate students and researchers interested in
integrable systems and their relations to differential geometry,
topology, algebraic geometry, and physics.
The second volume from this conference also available from the
AMS is Integrable Systems, Topology, and Physics, Volume 309 CONM/309in
the Contemporary Mathematics series. The forthcoming third volume
will be published by the Mathematical Society of Japan and will
be available outside of Japan from the AMS in the Advanced
Studies in Pure Mathematics series.
Contents
N. Ando -- The index of an isolated umbilical
point on a surface
J. Bolton -- The toda equations and equiharmonic
maps of surfaces into flag manifolds
J.-M. Burel and E. Loubeau -- $p$-harmonic
morphisms: The $1<p<2$ case and some
non-trivial examples
F. Burstall, F. Pedit, and U. Pinkall --
Schwarzian derivatives and flows of surfaces
V. De Smedt and S. Salamon -- Anti-self-dual
metrics on Lie groups
J. Dorfmeister, J.-i. Inoguchi, and M. Toda
-- Weierstras-type representation of timelike
surfaces with constant mean curvature
N. Ejiri -- A differential-geometric Schottky
problem, and minimal surfaces in tori
E. V. Ferapontov -- Surfaces in 3-space possessing
nontrivial deformations which preserve the
shape operator
F. Helein and P. Romon -- Hamiltonian stationary
Lagrangian surfaces in Hermitian symmetric
spaces
H. Hu -- Line congruences and integrable
systems
X. Jiao -- Factorizations of harmonic maps
of surfaces into Lie groups by singular dressing
actions
H. Jin and X. Mo -- On submersive $p$-harmonic
morphisms and their stability
K. Kiyohara -- On Kahler-Liouville manifolds
M. Kokubu, M. Umehara, and K. Yamada -- Minimal
surfaces that attain equality in the Chern-Osserman
inequality
V. S. Matveev -- Low dimensional manifolds
admitting metrics with the same geodesics
Y. Ohnita and S. Udagawa -- Harmonic maps
of finite type into generalized flag manifolds,
and twistor fibrations
J. Park -- Submanifolds associated to Grassmannian
systems
Y. Sakane and T. Yamada -- Harmonic cohomology
groups of compact symplectic nilmanifolds
B. A. Springborn -- Bonnet pairs in the 3-sphere
M. S. Tanaka -- Subspaces in the category
of symmetric spaces
H. Tasaki -- Integral geometry of submanifolds
of real dimension two and codimension two
in complex projective spaces
J. C. Wood -- Jacobi fields along harmonic
maps
H. Wu -- Denseness of plain constant mean
curvature surfaces in dressing orbits
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume: 308
Publication Year: 2002
ISBN: 0-8218-2938-6
Paging: 349 pp.
Binding: Softcover
Asterisque 278 (2002), xii+248 pages
Resume :
Ce volume est le premier d'une serie de trois consacres aux
methodes p-adiques en geometrie arithmetique. Les themes abordes
dans ce volume touchent a la theorie des groupes formels et de
leurs deformations, au programme de Langlands p-adique, et a la
geometrie hyperbolique p-adique.
Mots clefs : Courbe hyperbolique, champ de modules,
uniformisation fuchsienne, uniformisation de Bers, p-adique,
theorie de Serre-Tate, relevement canonique, representation
galoisienne, action exterieure de Galois, groupe de Teichmuller,
espace symetrique p-adique, transformee integrale, residu,
representation p-adique, groupe p-divisible, cristaux, modules de
Cartier, biextension
Abstract:
p-adic cohomologies and arithmetic applications (I)
This volume is the first of three dealing with p-adic methods in
arithmetic geometry. The themes appearing in this volume include
the theory of formal groups and their deformations, the p-adic
Langlands program, and the p-adic hyperbolic geometry.
Key words: Hyperbolic curve, moduli stack, uniformization theory,
Fuchsian uniformization, Bers uniformization, p-adic, Serre-Tate
theory, canonical liftings, Galois representations, outer Galois
actions, Teichmuller group, p-adic symmetric space, integral
transform, residue, p-adic representation, p-divisible group,
crystalline cohomology
Class. math. : 11F85, 14F30, 14F40, 14H10, 14L05, 22E50
ISBN : 2-85629-115-5
Asterisque 279 (2002), xiv+370 pages
Resume :
Ce volume est le second d'une serie de trois consacres aux
methodes p-adiques en geometrie arithmetique. Il est centre
autour des problemes de construction des cohomologies p-adiques
et des theoremes de comparaison entre ces cohomologies: geometrie
logarithmique, cohomologie cristalline, D-modules arithmetiques,
equations differentielles p-adiques, et theoremes de comparaison
de Faltings et Tsuji.
Mots clefs : Puissances divisees, operateur differentiel, -module,
isocristal, surconvergence, complexe parfait, operation
cohomologique, cohomologie de de Rham, cohomologie cristalline,
cohomologie rigide, Frobenius, variete caracteristique, module
holonome, cohomologie etale, reduction semi-stable, site
syntomique, coefficients p-adiques, cohomologie etale p-adique,
geometrie logarithmique, monoide, log structure, log schema,
Kummer, log etale, log lisse, diviseur a croisements normaux,
revetement, groupe fondamental, cohomologie de Betti, cohomologie
-adique, modere, log eclatement, variete torique, acyclicite,
cycles proches, cycles evanescents, monodromie, poids, regulier,
purete, changement de base, representation p-adique
Abstract:
p-adic cohomologies and arithmetic applications (II)
This volume is the second of three dealing with p-adic methods in
arithmetic geometry. It is centered around the construction of p-adic
cohomology theories and comparaison theorems between these
cohomologies : logarithmic geometry, crystalline cohomology,
arithmetic D-modules, p-adic differential equations, and
comparison theorems of Faltings and Tsuji.
Key words: Divided powers, differential operator, -module,
isocrystal, overconvergence, perfect complex, cohomological
operation, de Rham cohomology, crystalline cohomology, rigid
cohomology, Frobenius, characteristic variety, holonomic module,
etale cohomology, semi-stable reduction, syntomic site, p-adic
coefficients, p-adic etale cohomology, logarithmic geometry,
monoid, log structure, log scheme, Kummer, log etale, log smooth,
divisor with normal crossings, covering, fundamental group, Betti
cohomology, -adic cohomology, tame, log blow-up, toric variety,
acyclicity, nearby cycles, vanishing cycles, monodromy, weights,
regular, purity, base change, p-adic representation
Class. math. : 11G10, 11G25, 11S20, 12H25, 13N10, 14A99, 14D05,
14D06, 14D10, 14E05, 14E20, 14E22, 14F10, 14F20, 14F30, 14F35, 14F40,
14G20, 14G22, 16S32, 32C38
ISBN : 2-85629-117-1