Edited by: R. Parimala, Tata Institute of Fundamental Research, Mumbai, India

Algebra, Arithmetic and Geometry Mumbai 2000 (Parts I and II)

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

Edited by: Ricardo Weder, IIMAS-UNAM, Mexico City, Mexico, Pavel Exner, Czech Academy of Sciences, Prague, Czech Republic, and Benoit Grebert, University of Nantes, France

Mathematical Results in Quantum Mechanics

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

Edited by: Eric D'Hoker, University of California, Los Angeles, CA, Duong Phong, Columbia University, New York, NY, and Shing-Tung Yau, Harvard University, Cambridge, MA

Mirror Symmetry IV

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

Edited by: Yu. M. Suhov, University of Cambridge, England, and Institute for Information Transmission Problems, Moscow, Russia

Analytic Methods in Applied Probability: In Memory of Fridrikh Karpelevich

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