A publication of the Tata Institute of Fundamental Research.
Description
This volume contains papers by invited speakers at the
International Colloquium on Algebra, Arithmetic and Geometry,
held at the Tata Institute of Fundamental Research (Mumbai, India)
in January 2000. The articles present the latest developments in
a broad variety of topics from algebraic geometry, group theory,
and K-theory. It is suitable for graduate students and research
mathematicians interested in those areas.
Contents
Part I
S. S. Abhyankar -- Symplectic groups and permutation polynomials
L. L. Avramov and S. Iyengar -- Homological criteria for regular
homomorphisms and for locally complete intersection homomorphisms
P. Barquero and A. Merkurjev -- Norm principle for reductive
algebraic groups
S. M. Bhatwadekar and R. Sridharan -- On Euler classes and stably
free projective modules
J. Biswas, G. Dayal, K. H. Paranjape, and G. V. Ravindra --
Higher Abel-Jacobi maps
S. Bloch and V. Srinivas -- Enriched Hodge structures
J.-L. Colliot-Thelene, M. Ojanguren, and R. Parimala -- Quadratic
forms over fraction fields of two-dimensional Henselian rings and
Brauer groups of related schemes
E. M. Friedlander and M. E. Walker -- Semi-topological K-theory
of real varieties
Part II
J. Herzog and E. Sbarra -- Sequentially Cohen-Macaulay modules
and local cohomology
W. van der Kallen -- From Mennicke symbols to Euler class groups
M.-A. Knus, R. Parimala, and R. Sridharan -- On generic triality
V. B. Mehta and S. Subramanian -- On the Harder-Narasimhan
filtration of principal bundles
V. B. Mehta and A. J. Parameswaran -- Geometry of low height
representations
M. Miyanishi and K. Masuda -- Generalized Jacobian conjecture and
related topics
N. M. Kumar -- Construction of rank two vector bundles on
projective spaces
M. V. Nori -- Constructible sheaves
M. P. Murthy -- Cancellation problem for projective modules over
certain affine algebras
V. L. Popov -- Self-dual algebraic varieties and nilpotent orbits
P. C. Roberts -- Intersection multiplicities and dimension
inequalities
P. Russell -- Some formal aspects of the theorems of Mumford-Ramanujam
R. Sujatha -- Euler-Poincare characteristics of p-adic Lie groups
and arithmetic
A. Suslin -- On the vanishing of H_3(SL_2(A,I), \mathbb{Z}/l)
Details:
Series: Tata Institute of Fundamental Research
Publication Year: 2002
ISBN: 81-7319-476-9
Paging: 651 pp.
Binding: Hardcover
Description
This book contains contributions presented
at the conference,
"QMath-8: Mathematical Results in Quantum
Mechanics",
held at Universidad Nacional Autonoma de
Mexico in December 2001.
The articles cover a wide range of mathematical
problems and
focus on various aspects of quantum mechanics,
quantum field
theory, and nuclear physics. Topics vary
from spectral properties
of the Schrodinger equation of various quantum
systems to the
analysis of quantum computation algorithms.
The book is suitable for graduate students
and research
mathematicians interested in the mathematical
aspects of quantum
mechanics.
Contents
R. Adami -- Blow-up for Schrodinger equation
with pointwise
nonlinearity
J.-M. Barbaroux, M. Dimassi, and J.-C. Guillot
-- Quantum
electrodynamics of relativistic bound states
with cutoffs. II
F. Bentosela and M. Tater -- Scattering by
a slab: An exact
calculation
X. Blanc and C. Le Bris -- Crystalline order
in one dimensional
Thomas-Fermi type models
J. Bourgain -- New results on the spectrum
of lattice Schrodinger
operators and applications
A. L. Bukhgeim, G. V. Dyatlov, and G. Uhlmann
-- Reconstruction
of the memory from partial boundary measurements
R. E. Cardiel and P. I. Naumkin -- Asymptotics
for nonlinear
dissipative equations in the super critical
case
J.-M. Combes, P. D. Hislop, and E. Soccorsi
-- Edge states for
quantum Hall Hamiltonians
M. Combescure and D. Robert -- A semiclassical
approach in linear
response theory
J. Cruz-Sampedro -- Wigner-von Neumann-like
potentials
M. Demuth and A. Noll -- Equilibrium potentials
in scattering
theory
J. Dittrich and J. Kriz -- Straight quantum
waveguides with
combined boundary conditions
V. Enss, V. Kostrykin, and R. Schrader --
Perturbation theory for
the quantum time-evolution in rotating potentials
L. Erdos and V. Vougalter -- Two dimensional
Pauli operator via
scalar potential
M. J. Esteban and E. Sere -- A max-min principle
for the ground
state of the Dirac-Fock functional
S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof,
and T.
Sorensen -- On the regularity of the density
of electronic wave
functions
C. Hainzl -- Enhanced binding through coupling
to a photon field
B. C. Hall and J. J. Mitchell -- The large
radius limit for
coherent states on spheres
I. Herbst and E. Skibsted -- Quantum scattering
for potentials
homogeneous of degree zero
W. Kirsch and I. Veselic -- Existence of
the density of states
for one-dimensional alloy-type potentials
with small support
V. Kostrykin and R. Schrader -- Statistical
ensembles and density
of states
M. Kudryavtsev -- The Cauchy problem for
the Toda lattice with a
class of non-stabilized initial data
A. Laptev, S. Naboko, and O. Safronov --
Absolutely continuous
spectrum of Jacobi matrices
E. H. Lieb and M. Loss -- Stability of matter
in relativistic
quantum electrodynamics
M. Mantoiu and R. Purice -- The algebra of
observables in a
magnetic field
D. B. Pearson -- Recent developments in value
distribution theory
for Schrodinger operators on the half line
D. Robert -- Long time propagation results
in quantum mechanics
M. B. Ruskai -- Comments on adiabatic quantum
algorithms
A. Sacchetti -- Tunneling destruction for
a nonlinear Schrodinger
equation
R. Seiringer -- Symmetry breaking in a model
of a rotating Bose
gas
S. B. Sontz -- Euler's constant in Segal-Bargmann
analysis
A. Tip -- Maxwell with a touch of Schrodinger
J. H. Toloza -- Exponentially accurate semiclassical
asymptotics
C. van der Mee and V. Pivovarchik -- Some
properties of the
eigenvalues of a Schrodinger equation with
energy-dependent
potential
C. Villegas-Blas -- The Bargmann transform
for L^2(S^3) and
regularization of the Kepler problem
K. Yajima and G. Zhang -- Schrodinger equations
with
superquadratic potentials
K. Yoshitomi -- Band spectrum of the Laplacian
on a slab with the
Dirichlet boundary condition on a grid
Other talks
Participants
Details:
Series: Contemporary Mathematics, Volume:
307
Publication Year: 2002
ISBN: 0-8218-2900-9
Paging: 350 pp.
Binding: Softcover
Description
This book presents contributions of participants of a workshop
held at the Centre de Recherches Mathematiques (CRM), University
of Montreal. It can be viewed as a sequel to Mirror Symmetry I (1998),
Mirror Symmetry II (1996), and Mirror Symmetry III (1999),
copublished by the AMS and International Press.
The volume presents a broad survey of many of the noteworthy
developments that have taken place in string theory, geometry,
and duality since the mid 1990s. Some of the topics emphasized
include the following: Integrable models and supersymmetric gauge
theories; theory of M- and D-branes and noncommutative geometry;
duality between strings and gauge theories; and elliptic genera
and automorphic forms. Several introductory articles present an
overview of the geometric and physical aspects of mirror symmetry
and of corresponding developments in symplectic geometry. The
book provides an efficient way for a very broad audience of
mathematicians and physicists to explore the frontiers of
research into this rapidly expanding area.
Contents
Calabi-Yau Manifolds, Mirror Symmetry, and Symplectic Geometry
B. H. Lian, K. Liu, and S.-T. Yau -- A survey of mirror principle
B. R. Greene -- Mirror symmetry: aspects of the first 10 years
W.-D. Ruan -- Lagrangian torus fibrations of Calabi-Yau
hypersurfaces in toric varieties and SYZ mirror symmetry
conjecture
G. Liu -- Moduli space of stable maps
F. Lalonde and D. McDuff -- Cohomological properties of ruled
symplectic structures
Supersymmetric gauge theories and integrable models
J. C. Hurtubise -- Spectral Lax pairs and Calogero-Moser systems
I. P. Ennes, C. Lozano, S. G. Naculich, H. Rhedin, and H. J.
Schnitzer -- M-theory tested by {\mathcal {N}}=2 Seiberg-Witten
theory
I. P. Ennes, C. Lozano, S. G. Naculich, and H. J. Schnitzer --
Seiberg-Witten curves for elliptic models
I. Krichever and K. L. Vaninsky -- The periodic and open Toda
lattice
J.-L. Gervais -- Exact integration methods for supersymmetric
Yang-Mills theory
M-theory, D-branes, and non-commutative geometry
R. C. Meyers -- Nonabelian D-branes and noncommutative geometry
P. Pouliot -- Evidence for winding states in noncommutative
quantum field theory
K. G. Savvidy -- The discrete bound state spectrum of the
rotating D0-brane system, and its decay by emission of Ramond-Ramond
field radiation
F. Denef -- On the correspondence between D-branes and stationary
supergravity solutions of type II Calabi-Yau compactifications
M. Faux, D. Lust, and B. A. Ovrut -- Phase-transition and tensor
dynamics in M-theory
N. A. Obers and B. Pioline -- Duality, Eisenstein series and
exact thresholds
Strings, gauge theories, and AdS/CFT correspondence
E. Witten and S.-T. Yau -- Connectedness of the boundary in the
AdS/CFT correspondence
S.-T. Yau -- A note on the topology of the boundary in the AdS/CFT
correspondence
M. Porrati and A. Starinets -- Holographic duals of 4D field
theories
D. Kabat, G. Lifschytz, and D. A. Lowe -- Black hole
thermodynamics from calculations in strongly-coupled gauge theory
O. Lunin and S. D. Mathur -- Correlation functions for orbifolds
of the type M^N/S^N
Elliptic genera and automorphic forms
L. A. Borisov and A. Libgober -- Elliptic genera of singular
varieties, orbifold elliptic genus and chiral de Rham complex
K. Liu and X. Ma -- On family rigidity theorems for Spin^{c}
manifolds
J. Jorgenson and A. Todorov -- Aample divisors, automorphic forms
and Shafarevich's conjecture
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 33
Publication Year: 2002
ISBN: 0-8218-3335-9
Paging: 381 pp.
Binding: Hardcover
Description
This volume is dedicated to F. I. Karpelevich, an outstanding
Russian mathematician who made important contributions to applied
probability theory. The book contains original papers focusing on
several areas of applied probability and its uses in modern
industrial processes, telecommunications, computing, mathematical
economics, and finance.
It opens with a review of Karpelevich's contributions to applied
probability theory and includes a bibliography of his works.
Other articles discuss queueing network theory, in particular, in
heavy traffic approximation (fluid models).
The book is suitable for graduate students, theoretical and
applied probabilists, computer scientists, and engineers.
Contents
A. Ya. Kreinin and Y. Suhov -- Karpelevich's contribution to
applied probability
O. J. Boxma, S. Schlegel, and U. Yechiali -- A note on an M/G/1
queue with a waiting server, timer, and vacations
S. Foss and S. Zachary -- Asymptotics for the maximum of a
modulated random walk with heavy-tailed increments
J. M. Harrison -- Stochastic networks and activity analysis
V. Kalashnikov -- Stability bounds for queueing models in terms
of weighted metrics
F. I. Karpelevich, V. A. Malyshev, A. I. Petrov, S. A. Pirogov,
and A. N. Rybko -- Context-free evolution of words
M. Kelbert, S. Rachev, and Y. Suhov -- The maximum of a tree-indexed
random process, with applications
J. Martin -- Stochastic bounds for fast Jackson networks
M. Menshikov and D. Petritis -- Markov chains in a wedge with
excitable boundaries
M. Mitzenmacher and B. Vocking -- Selecting the shortest of two
queues, improved
A. N. Rybko, A. L. Stolyar, and Y. M. Suhov -- Stability of
global LIFO networks
S. Shakkottai and A. L. Stolyar -- Scheduling for multiple flows
sharing a time-varying channel: The exponential rule
M. G. Shur -- New ratio limit theorems for Markov chains
E. J. Thomas -- Stability of patchwork-JSQ feedback networks
Details:
Series: American Mathematical Society Translations--Series 2,Volume:
207
Publication Year: 2002
ISBN: 0-8218-3306-5
Paging: 217 pp.
Binding: Hardcover