Contemporary Mathematics, Volume: 412
2006; 333 pp; softcover
ISBN-10: 0-8218-3840-7
ISBN-13: 978-0-8218-3840-2
Its topics include asymptotic formulas for the ground-state
energy of fermionic gas, renormalization ideas in quantum field
theory from perturbations of the free Hamiltonian on the circle,
J-selfadjoint Dirac operators, spectral theory of Schrodinger
operators, inverse problems, isoperimetric inequalities in
quantum mechanics, Hardy inequalities, and non-adiabatic
transitions.
Excellent survey articles on Dirichlet-Neumann inverse problems
on manifolds (by Uhlmann), numerical investigations associated
with Laplacian eigenvalues on planar regions (by Trefethen),
Snell's law and propagation of singularities in the wave equation
(by Vasy), random operators on tree graphs (by Aizenmann) make
this book interesting and valuable for graduate students, young
mathematicians, and physicists alike.
Readership
Graduate students and research mathematicians interested in
quantum theory, spectral theory of Schroedinger operators,
inverse problems, and inverse algorithms.
Table of Contents
M. Aizenman, R. Sims, and S. Warzel -- Fluctuation based proof of
the stability of ac spectra of random operators on tree graphs
T. Aktosun and R. Weder -- The Borg-Marchenko theorem with a
continuous spectrum
M. H. Annaby, G. Freiling, and I. A. Soliman -- Sampling theorems
associated with differential operators iterated from lower order
ones
W. Arendt, G. R. Goldstein, and J. A. Goldstein -- Outgrowths of
Hardy's inequality
A. A. Balinsky and A. E. Tyukov -- On Hardy type inequalities
R. D. Benguria -- A nonlinear fourth-order minimization problem
B. M. Brown, M. Jais, and P. C. Kalmbach -- A variational
approach to inverse problems for anistropic systems
S. Clark and F. Gesztesy -- On self-adjoint and J-self-adjoint
Dirac type operators: A case study
P. Exner -- Necklaces with interacting beads: Isoperimetric
problems
C. Fox, V. Oleinik, and B. Pavlov -- A Dirichlet-to-Neumann map
approach to resonance gaps and bands of periodic networks
G. Gallavotti -- Resonances and summation of divergent series
G. A. Hagedorn and A. Joye -- Recent results on non-adiabatic
transitions in quantum mechanics
R. Hempel -- Schrodinger operators with strong magnetic fields of
compact support
D. Hinton and M. L. McCarthy -- Optimization of the minimum
eigenvalue for a class of second order differential operators
R. Lavine -- Time of arrival in quantum mechanics and the quantum
zeno effect
E. H. Lieb, R. Seiringer, and J. P. Solovej -- Ground-state
energy of a dilute Fermi gas
L. Pestov and G. Uhlmann -- The scattering relation and the
Dirichlet-to-Neumann map
N. Rohrl -- Recovering boundary conditions in inverse Sturm-Liouville
problems
A. Rybkin -- Preservation of the absolutely continuous spectrum:
Some extensions of a result by Molchanov-Novitskii-Vainberg
V. Tkachenko -- Expansions associated with 1d periodic
differential operators of order 4
L. N. Trefethen and T. Betcke -- Computed eigenmodes of planar
regions
A. Vasy -- Geometric optics and the wave equation on manifolds
with corners
AMS/IP Studies in Advanced Mathematics, Volume: 37
2006; 239 pp; softcover
ISBN-10: 0-8218-4198-X
ISBN-13: 978-0-8218-4198-3
This book consists of five chapters which give comprehensive
introductions to Lie groups, Lie algebras, arithmetic groups and
reduction theories, cohomology of arithmetic groups, and the
Petersson and Kuznetsov trace formulas.
Titles in this series are copublished with International Press,
Cambridge, MA.
Readership
Graduate students and research mathematicians interested in lie
groups, automorphics forms, and number theory.
Table of Contents
A. Borel -- Lie groups and linear algebraic groups I. Complex and
real groups
A. Borel -- Introduction to the cohomology of arithmetic groups
L. Ji -- Lectures on locally symmetric spaces and arithmetic
groups
J. Liu and Y. Ye -- Petersson and Kuznetsov trace formulas
L. Saper -- On the cohomology of locally symmetric spaces and of
their compactifications
Proceedings of Symposia in Pure Mathematics, Volume: 74
2006; 371 pp; hardcover
ISBN-10: 0-8218-3838-5
ISBN-13: 978-0-8218-3838-9
The appearance of mapping class groups in mathematics is
ubiquitous. The book presents 23 papers containing problems about
mapping class groups, the moduli space of Riemann surfaces,
Teichmuller geometry, and related areas. Each paper focusses
completely on open problems and directions. The problems range in
scope from specific computations, to broad programs. The goal is
to have a rich source of problems which have been formulated
explicitly and accessibly.
The book is divided into four parts. Part I contains problems on
the combinatorial and (co)homological group-theoretic aspects of
mapping class groups, and the way in which these relate to
problems in geometry and topology. Part II concentrates on
connections with classification problems in 3-manifold theory,
the theory of symplectic 4-manifolds, and algebraic geometry. A
wide variety of problems, from understanding billiard
trajectories to the classification of Kleinian groups, can be
reduced to differential and synthetic geometry problems about
moduli space. Such problems and connections are discussed in Part
III. Mapping class groups are related, both concretely and
philosophically, to a number of other groups, such as braid
groups, lattices in semisimple Lie groups, and automorphism
groups of free groups. Part IV concentrates on problems
surrounding these relationships.
This book should be of interest to anyone studying geometry,
topology, algebraic geometry or infinite groups. It is meant to
provide inspiration for everyone from graduate students to senior
researchers.
Readership
Graduate students and research mathematicians interested in
mapping class groups and applications.
Table of Contents
I. Cohomological, combinatorial and algebraic structure
M. Bestvina -- Four questions about mapping class groups
B. Farb -- Some problems on the mapping class group and moduli
space
R. Hain -- Finiteness and Torelli spaces
N. V. Ivanov -- Fifteen problems about the mapping class groups
M. Korkmaz -- Problems on homomorphisms of mapping class groups
I. Madsen -- The mapping class group and homotopy theory
R. C. Penner -- Probing mapping class groups using arcs
B. Wajnryb -- Relations in the mapping class group
II. Connections with 3-manifolds, symplectic geometry and
algebraic geometry
D. Auroux -- Mapping class group factorizations and symplectic 4-manifolds:
Some open problems
J. S. Birman -- The topology of 3-manifolds, Heegaard distances
and the mapping class group of a 2-manifold
S. K. Donaldson -- Lefschetz pencils and mapping class groups
P. Lochak and L. Schneps -- Open problems in Grothendieck-Teichmuller
theory
III. Geometry and dynamical aspects
W. M. Goldman -- Mapping class group dynamics on surface group
representations
U. Hamenstadt -- Geometric properties of the mapping class group
P. Hubert, H. Masur, T. Schmidt, and A. Zorich -- Problems on
billiards, flat surfaces and translation surfaces
L. Mosher -- Problems in the geometry of surface group extensions
A. W. Reid -- Surface subgroups of mapping class groups
S. A. Wolpert -- Weil-Petersson perspectives
IV. Braid groups, Out(F_n) and other related groups
S. Bigelow -- Braid groups and Iwahori-Hecke algebras
M. R. Bridson and K. Vogtmann -- Automorphism groups of free
groups, surface groups and free abelian groups
F. R. Cohen -- Problems: Braid groups, homotopy, cohomology, and
representations
S. Morita -- Cohomological structure of the mapping class group
and beyond
L. Paris -- From braid groups to mapping class groups
Contemporary Mathematics, Volume: 413
2006; 254 pp; softcover
ISBN-10: 0-8218-3924-1
ISBN-13: 978-0-8218-3924-9
The book contains several well-written accessible survey papers
in many interrelated areas of current research. These areas cover
various aspects of the representation theory of Lie algebras,
finite groups of Lie types, Hecke algebras, and Lie superalgebras.
Geometric methods have been instrumental in representation
theory, and the proceedings include surveys on geometric as well
as combinatorial constructions of the crystal basis for
representations of quantum groups. Humphreys' paper outlines
intricate connections among irreducible representations of
certain blocks of reduced enveloping algebras of semi-simple Lie
algebras in positive characteristic left cells in two sided cells
of affine Weyl groups, and the geometry of the nilpotent orbits.
All these papers provide the reader with a broad picture of the
interaction of many different research areas and should be
helpful to those who want to have a glimpse of current research
involving representation theory.
Readership
Graduate students and research mathematicians interested in
various aspects of representation theory.
Table of Contents
C. P. Bendel, D. K. Nakano, and C. Pillen -- Extensions for
finite groups of Lie type II: Filtering the truncated induction
functor
B. Deng and J. Du -- Algebras, representations and their derived
categories over finite fields
Y. Hashimoto, M. Kaneda, and D. Rumynin -- On localization of D-modules
J. E. Humphreys -- Representations of reduced enveloping algebras
and cells in the affine Weyl group
S.-J. Kang, J.-A. Kim, and D.-U. Shin -- Nakajima's monomials and
crystal bases
G. Karaali -- A new Lie bialgebra structure on sl(2,1)
J. Kujawa -- The Steinberg tensor product theorem for GL(m|n)
Z. Lin and H. Rui -- Cyclotomic q-Schur algebras and Schur-Weyl
duality
T. Nakashima -- Geometric crystals and affine crystals
C. Pillen -- Self-extensions for finite symplectic groups via
algebraic groups
A. Premet and H. Strade -- Classification of finite dimensional
simple Lie algebras in prime characteristics
E. C. Rowell -- From quantum groups to unitary modular tensor
categories
J. Xiao and G. Zhang -- A trip from representations of the
Kronecker quiver to canonical bases of quantum affine algebras