Fields Institute Communications, Volume: 50
2007; 404 pp; hardcover
ISBN-10: 0-8218-4273-0
ISBN-13: 978-0-8218-4273-7
This book covers a wide range of phenomena in the natural
sciences dominated by notions of universality and renormalization.
The contributions in this volume are equally broad in their
approach to these phenomena, offering the mathematical as well as
the perspective of the applied sciences. They explore
renormalization theory in quantum field theory and statistical
physics, and its connections to modern mathematics as well as
physics on scales from the microscopic to the macroscopic.
Readership
Graduate students and research mathematicians interested in
quantum field theory, statistical physics, physics and number
theory, nonlinear dynamics, probability,geometic function theory,
differential equations.
Table of Contents
S. Arnone, T. R. Morris, and O. J. Rosten -- Manifestly gauge
invariant exact renormalization groups
R. O. Bauer -- SLE(8/3) and Brownian excursions in annuli
V. Beffara -- Cardy's formula on the triangular lattice, the easy
way
K. Ebrahimi-Fard and L. Guo -- Rota-Baxter algebras in
renormalization of perturbative quantum field theory
J. A. Gracey -- Practicalities of renormalizing quantum field
theories
S. Hollands -- Quantum field theory in curved spacetime
A. R. Its, B.-Q. Jin, and V. E. Korepin -- Entropy of $XY$ spin
chain and block Toeplitz determinants
N.-G. Kang -- On the quantitative boundary behavior of SLE
M. J. Kozdron and G. F. Lawler -- The configurational measure on
mutually avoiding SLE paths
D. Kreimer -- Dyson-Schwinger equations: From Hopf algebra to
number theory
G. F. Lawler and J. R. Lind -- Two-sided $SLE_{8/3}$ and the
infinite self-avoiding polygon
D. G. C. McKeon -- Using the renormalization group
J. Palmer -- Short distance behavior of scaling functions for the
planar ising model
I. Todorov -- Constructing conformal field theory models
S. Weinzierl -- The art of computing loop integrals
J. Zinn-Justin -- The transition temperature of the weakly
interacting Bose gas
Mathematical Surveys and Monographs, Volume: 135
2007; 536 pp; hardcover
ISBN-10: 0-8218-3946-2
ISBN-13: 978-0-8218-3946-1
This book gives a presentation of topics in Hamilton's Ricci flow
for graduate students and mathematicians interested in working in
the subject. The authors have aimed at presenting technical
material in a clear and detailed manner. In this volume,
geometric aspects of the theory have been emphasized. The book
presents the theory of Ricci solitons, Kahler-Ricci flow,
compactness theorems, Perelman's entropy monotonicity and no
local collapsing, Perelman's reduced distance function and
applications to ancient solutions, and a primer of 3-manifold
topology. Various technical aspects of Ricci flow have been
explained in a clear and detailed manner. The authors have tried
to make some advanced material accessible to graduate students
and nonexperts. The book gives a rigorous introduction to
Perelman's work and explains technical aspects of Ricci flow
useful for singularity analysis. Throughout, there are
appropriate references so that the reader may further pursue the
statements and proofs of the various results.
Readership
Graduate students and research mathematicians interested in
geometric analysis, specifically, the use of Ricci flow to study
the geometry and topology of three-dimensional manifolds and
Perelman's methods for proving the Poincare conjecture.
Contents
Mathematical Surveys and Monographs, Volume: 137
2007; 222 pp; hardcover
ISBN-10: 0-8218-4177-7
ISBN-13: 978-0-8218-4177-8
The systole of a compact metric space $X$ is a metric invariant
of $X$, defined as the least length of a noncontractible loop in
$X$. When $X$ is a graph, the invariant is usually referred to as
the girth, ever since the 1947 article by W. Tutte. The first
nontrivial results for systoles of surfaces are the two classical
inequalities of C. Loewner and P. Pu, relying on integral-geometric
identities, in the case of the two-dimensional torus and real
projective plane, respectively. Currently, systolic geometry is a
rapidly developing field, which studies systolic invariants in
their relation to other geometric invariants of a manifold.
This book presents the systolic geometry of manifolds and
polyhedra, starting with the two classical inequalities, and then
proceeding to recent results, including a proof of M. Gromov's
filling area conjecture in a hyperelliptic setting. It then
presents Gromov's inequalities and their generalisations, as well
as asymptotic phenomena for systoles of surfaces of large genus,
revealing a link both to ergodic theory and to properties of
congruence subgroups of arithmetic groups. The author includes
results on the systolic manifestations of Massey products, as
well as of the classical Lusternik-Schnirelmann category.
Readership
Graduate students and research mathematicians interested in new
methods in differential geometry and topology.
Contents
Contemporary Mathematics, Volume: 425
2007; 150 pp; softcover
ISBN-10: 0-8218-3819-9
ISBN-13: 978-0-8218-3819-8
The articles in this book are based on talks given at the North
Texas Logic Conference in October of 2004. The main goal of the
editors was to collect articles representing diverse fields
within logic that would both contain significant new results and
be accessible to readers with a general background in logic.
Included in the book is a problem list, jointly compiled by the
speakers, that reflects some of the most important questions in
various areas of logic. This book should be useful to graduate
students and researchers alike across the spectrum of
mathematical logic.
Readership
Graduate students and research mathematicians interested in logic.
Table of Contents
J. R. Steel -- A stationary-tower-free proof of the derived model
theorem
I. Farah -- A proof of the $\Sigma^2_1$-absoluteness theorem
S. Bold and B. Lowe -- A simple inductive measure analysis for
cardinals under the axiom of determinacy
S. Lempp and T. Slaman -- The complexity of the index sets of
$\aleph_0$-cateogrical theories and of Ehrenfeucht theories
W. Calvert, S. S. Goncharov, and J. F. Knight -- Computable
structures of Scott rank $\omega_1^{CK}$ in familiar classes
R. Solomon -- Thin classes of separating sets
A. Blass -- Voting rules for infinite sets and boolean algebras
B. Kastermans -- Very mad families
C. M. Boykin and S. Jackson -- Borel boundedness and the lattice
rounding property
S. Gao, A. W. Miller, and W. A. R. Weiss -- Steinhaus sets and
Jackson sets
S. Gao, S. Jackson, and Y. Zhang -- A problem list
Contemporary Mathematics, Volume: 426
2007; 404 pp; softcover
ISBN-10: 0-8218-3766-4
ISBN-13: 978-0-8218-3766-5
While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM
Summer Research Conference sought to reach out to a rather
distinct, yet scientifically related, research community in
mathematics interested in PDE-based dynamical systems. Indeed,
this community is also involved in the study of dynamical
properties and asymptotic long-time behavior (in particular,
stability) of PDE-mixed problems. It was the editors' conviction
that the time had become ripe and the circumstances propitious
for these two mathematical communities--that of PDE control and
optimization theorists and that of dynamical specialists--to come
together in order to share recent advances and breakthroughs in
their respective disciplines. This conviction was further
buttressed by recent discoveries that certain energy methods,
initially devised for control-theoretic a-priori estimates, once
combined with dynamical systems techniques, yield wholly new
asymptotic results on well-established, nonlinear PDE systems,
particularly hyperbolic and Petrowski-type PDEs.
These expectations are now particularly well reflected in the
contributions to this volume, which involve nonlinear parabolic,
as well as hyperbolic, equations and their attractors; aero-elasticity,
elastic systems; Euler-Korteweg models; thin-film equations;
Schrodinger equations; beam equations; etc. In addition, the
static topics of Helmholtz and Morrey potentials are also
prominently featured. A special component of the present volume
focuses on hyperbolic conservation laws, to take advantage of
recent theoretical advances with significant implications also on
applied problems. In all these areas, the reader will find state-of-the-art
accounts as stimulating starting points for further research.
Readership
Graduate students and research mathematicians interested in
partial differential equations and control theory.
Table of Contents
F. Ancona and A. Marson -- Asymptotic stabilization of systems of
conservation laws by controls acting at a single boundary point
G. Auchmuty -- Variational principles for finite-dimensional
initial value problems
G. Avalos and P. Cokeley -- Boundary and localized null
controllability of structurally damped elastic systems
A. V. Balakrishnan -- Nonlinear aeroelastic theory: Continuum
models
S. Benzoni-Gavage, R. Danchin, S. Descombes, and D. Jamet --
Stability issues in the Euler-Korteweg model
A. Bressan and W. Shen -- Optimality conditions for solutions to
hyperbolic balance laws
I. Chueshov and I. Lasiecka -- Long-time dynamics of a semilinear
wave equation with nonlinear interior/boundary damping and
sources of critical exponents
R. M. Colombo and M. Garavello -- On the $p$-system at a junction
A. V. Fursikov -- Analyticity of stable invariant manifolds of 1D-semilinear
parabolic equations
G. Hegarty and S. Taylor -- Boundary feedback stabilization of
nonlinear beam models
V. Isakov -- Increased stability in the continuation for the
Helmholtz equation with variable coefficient
J. R. King -- Microscale sensitivity in moving-boundary problems
for the thin-film equation
W. Littman and S. Taylor -- The heat and Schrodinger equations:
Boundary control with one shot
J. Serrin -- A remark on the Morrey potential
G. Todorova and B. Yordanov -- Nonlinear dissipative wave
equations with potential
R. Triggiani and X. Xu -- Pointwise Carleman estimates, global
uniqueness, observability, and stabilization for Schrodinger
equations on Riemannian manifolds at the $H^1(\Omega)$-level