Expected publication date is November 27, 2005
Description
This is a monograph on convexity properties of moment mappings in
symplectic geometry. The fundamental result in this subject is
the Kirwan convexity theorem, which describes the image of a
moment map in terms of linear inequalities. This theorem bears a
close relationship to perplexing old puzzles from linear algebra,
such as the Horn problem on sums of Hermitian matrices, on which
considerable progress has been made in recent years following a
breakthrough by Klyachko. The book presents a simple local model
for the moment polytope, valid in the "generic" case,
and an elementary Morse-theoretic argument deriving the Klyachko
inequalities and some of their generalizations. It reviews
various infinite-dimensional manifestations of moment convexity,
such as the Kostant type theorems for orbits of a loop group (due
to Atiyah and Pressley) or a symplectomorphism group (due to
Bloch, Flaschka and Ratiu). Finally, it gives an account of a new
convexity theorem for moment map images of orbits of a Borel
subgroup of a complex reductive group acting on a Kahler
manifold, based on potential-theoretic methods in several complex
variables.
This volume is recommended for independent study and is suitable
for graduate students and researchers interested in symplectic
geometry, algebraic geometry, and geometric combinatorics.
Contents
Introduction
The convexity theorem for Hamiltonian $G$-spaces
A constructive proof of the non-abelian convexity theorem
Some elementary examples of the convexity theorem
Kahler potentials and convexity
Applications of the convexity theorem
Bibliography
Details:
Series: CRM Monograph Series, Volume: 26
Publication Year: 2005
ISBN: 0-8218-3918-7
Paging: 82 pp.
Binding: Hardcover
Expected publication date is December 28, 2005
Description
This book contains a unique exposition intended to serve as an
introduction to functional analysis. Topics covered include
normed spaces and bounded operators, Banach spaces, polynormed
spaces and distributions, compact operators, $C^*$ algebra,
spectral theorems, Fourier transform, and more.
A distinguishing feature of the book is the wide use of the
language and elementary constructions of category theory, which
are explained in the opening chapter of the book. Among
nonstandard topics discussed in the book are the theory of Banach
tensor products, basics of quantum functional analysis, and Borel
operator calculus. General definitions and main results are
supplemented with many examples and exercises.
Prerequisites for the main part of the book include standard
undergraduate courses in algebra and analysis. It is suitable for
graduate students and researchers interested in functional
analysis.
Contents
Foundations: Categories and the like
Normed spaces and bounded operators ("Waiting for
completeness")
Banach spaces and their advantages
From compact spaces to Fredholm operators
Polynormed spaces, weak topologies, and generalized functions
At the gates of spectral theory
Hilbert adjoint operators and the spectral theorem
Fourier transform
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics, Volume: 71
Publication Year: 2005
ISBN: 0-8218-3552-1
Paging: approximately 496 pp.
Binding: Hardcover
Expected publication date is November 13, 2005
Description
This proceedings volume resulted from the John H. Barrett
Memorial Lecture Series held at the University of Tennessee (Knoxville).
The articles reflect recent developments in algebraic geometry.
It is suitable for graduate students and researchers interested
in algebra and algebraic geometry.
Contents
F. Campana and Q. Zhang -- Compact Kahler threefolds of $\pi_1$-general
type
S. D. Cutkosky and L. Ghezzi -- Completions of valuation rings
A. Ebin, D. Hur, A. Katz, and V. Shchogolev -- A new construction
of maximal curves
S. J. Kovacs -- Strong non-isotriviality and rigidity
S. J. Kovacs -- Spectral sequences associated to morphisms of
locally free sheaves
T. Luo and Q. Zhang -- Holomorphic forms on threefolds
K. Matsuki -- A note on toroidalization: The problem of
resolution of singularities of morphisms in the logarithmic
category
R. J. Pries -- Jacobians of quotients of Artin-Schreier curves
K. Schwede -- Gluing schemes and a scheme without closed points
Details:
Series: Contemporary Mathematics, Volume: 386
Publication Year: 2005
ISBN: 0-8218-3401-0
Paging: 172 pp.
Binding: Softcover
Expected publication date is November 2, 2005
Description
This volume contains articles based on talks given at the Robert
Brooks Memorial Conference on Geometry and Spectral Theory and
the Workshop on Groups, Geometry and Dynamics held at Technion -
the Israel Institute of Technology (Haifa).
Robert Brooks' (1952 - 2002) broad range of mathematical
interests is represented in the volume, which is devoted to
various aspects of global analysis, spectral theory, the theory
of Riemann surfaces, Riemannian and discrete geometry, and number
theory. A survey of Brooks' work has been written by his close
colleague, Peter Buser.
Also included in the volume are articles on analytic topics, such
as Szego's theorem, and on geometric topics, such as
isoperimetric inequalities and symmetries of manifolds.
The book is suitable for graduate students and researchers
interested in various aspects of geometry and global analysis.
This book is copublished with Bar-Ilan University.
Contents
P. Buser -- On the mathematical work of Robert Brooks
D. Blanc -- Moduli spaces of homotopy theory
R. Brooks and M. Monastyrsky -- K-regular graphs and Hecke
surfaces
P. Buser and K.-D. Semmler -- Isospectrality and spectral
rigidity of surfaces with small topology
I. Chavel -- Topics in isoperimetric inequalities
B. Farb and S. Weinberger -- Hidden symmetries and arithmetic
manifolds
H. M. Farkas -- Variants of the $3N+1$ conjecture and
multiplicative semigroups
U. Frauenfelder, V. Ginzburg, and F. Schlenk -- Energy capacity
inequalities via an action selector
K. Fujiwara -- On non-bounded generation of discrete subgroups in
rank-1 Lie group
C. Gordon, P. Perry, and D. Schueth -- Isospectral and
isoscattering manifolds: A survey of techniques and examples
M. G. Katz and C. Lescop -- Filling area conjecture, optimal
systolic inequalities, and the fiber class in abelian covers
E. Leichtnam -- An invitation to Deninger's work on arithmetic
zeta functions
A. Lubotzky -- Some more non-arithmetic rigid groups
R. G. Pinsky -- On domain monotonicity for the principal
eigenvalue of the Laplacian with a mixed Dirichlet-Neumann
boundary condition
B. Simon -- The sharp form of the strong Szego theorem
Details:
Series: Contemporary Mathematics, Volume: 387
Publication Year: 2005
ISBN: 0-8218-3710-9
Paging: 275 pp.
Binding: Softcover
Expected publication date is November 13, 2005
Description
A significant part of the 2004 Summer Research Conference on
Algebraic Geometry (Snowbird, UT) was devoted to lectures
introducing the participants, in particular, graduate students
and recent Ph.D.'s, to a wide swathe of algebraic geometry and
giving them a working familiarity with exciting, rapidly
developing parts of the field. One of the main goals of the
organizers was to allow the participants to broaden their
horizons beyond the narrow area in which they are working. A fine
selection of topics and a noteworthy list of contributors made
the resulting collection of articles a useful resource for
everyone interested in getting acquainted with the modern topic
of algebraic geometry.
The book consists of ten articles covering, among others, the
following topics: the minimal model program, derived categories
of sheaves on algebraic varieties, Kobayashi hyperbolicity,
groupoids and quotients in algebraic geometry, rigid analytic
varieties, and equivariant cohomology. Suitable for independent
study, this unique volume is intended for graduate students and
researchers interested in algebraic geometry.
Contents
C. Araujo -- Rationally connected varieties
C. Cadman, I. Coskun, K. Jabbusch, M. Joyce, S. J. Kovacs, M.
Lieblich, F. Sato, M. Szczesny, and J. Zhang -- A first glimpse
at the minimal model program
A. Caldararu -- Derived categories of sheaves: A skimming
I. Coskun -- The arithmetic and the geometry of Kobayashi
hyperbolicity
S. Grushevsky -- Multiplier ideals in algebraic geometry
D. Lehavi -- Mikhalkin's classification of $M$-curves in maximal
position with respect to three lines
M. Lieblich -- Groupoids and quotients in algebraic geometry
B. Osserman -- Two degeneration techniques for maps of curves
M. Papikian -- Rigid-analytic geometry and the uniformization of
abelian varieties
N. Proudfoot -- Geometric invariant theory and projective toric
varieties
J. S. Tymoczko -- An introduction to equivariant cohomology and
homology, following Goresky, Kottwitz, and MacPherson
Details:
Series: Contemporary Mathematics, Volume: 388
Publication Year: 2005
ISBN: 0-8218-3719-2
Paging: 188 pp.
Binding: Softcover