CRM Proceedings & Lecture Notes, Volume: 52
2010; 207 pp; softcover
ISBN-13: 978-0-8218-4778-7
Expected publication date is August 25, 2010.
This volume contains a collection of papers presented at the workshop on Spectrum and Dynamics held at the CRM in April 2008. In recent years, many new exciting connections have been established between the spectral theory of elliptic operators and the theory of dynamical systems. A number of articles in the proceedings highlight these discoveries. The volume features a diversity of topics, such as quantum chaos, spectral geometry, semiclassical analysis, number theory and ergodic theory. Apart from the research papers aimed at the experts, this book includes several survey articles accessible to a broad mathematical audience.
Graduate students and research mathematicians interested in PDEs on manifolds and dynamical systems with hyperbolic behavior.
S. Nonnenmacher -- Notes on the minicourse "Entropy of chaotic eigenstates"
A. Strohmaier -- Geometry of the high energy limit on differential operators on vector bundles
Y. A. Kordyukov -- Classical and quantum dynamics in transverse geometry of Riemannian foliations
L. Hillairet -- Eigenvalue variations and semiclassical concentration
H. Lapointe -- A remainder estimate for Weyl's law on Liouville tori
H. Donnelly -- Embedding eigenvalues for Cartan-Hadamard manifolds
B. Helffer and T. Hoffmann-Ostenhof -- On minimal partitions: New properties and applications to the disk
M. Pollicott -- Asymptotic vertex growth for graphs
D. Mayer and T. Muhlenbruch -- Nearest lambda_q-multiple fractions
R. Sharp -- Comparing length functions on free groups
Clay Mathematics Proceedings, Volume: 10
2010; approx. 440 pp; softcover
ISBN-13: 978-0-8218-4742-8
Expected publication date is September 17, 2010.
This book contains a wealth of material concerning two very active and
interconnected directions of current research at the interface of dynamics,
number theory and geometry. Examples of the dynamics considered are the
action of subgroups of textrm{SL}(n,mathbb{R}) on the space of unit volume
lattices in mathbb{R}^n and the action of textrm{SL}(2,mathbb{R}) or its
subgroups on moduli spaces of flat structures with prescribed singularities
on a surface of genus ge 2.
Topics covered include the following:
(a) Unipotent flows: non-divergence, the classification of invariant measures, equidistribution, orbit closures.
(b) Actions of higher rank diagonalizable groups and their invariant measures, including entropy theory for such actions.
(c) Interval exchange maps and their connections to translation surfaces, ergodicity and mixing of the Teichmuller geodesic flow, dynamics of rational billiards.
(d) Application of homogeneous flows to arithmetic, including applications to the distribution of values of indefinite quadratic forms at integral points, metric Diophantine approximation, simultaneous Diophantine approximations, counting of integral and rational points on homogeneous varieties.
(e) Eigenfunctions of the Laplacian, entropy of quantum limits, and arithmetic quantum unique ergodicity.
(f) Connections between equidistribution and automorphic forms and their
L-functions.
Graduate students and research mathematicians interested in the interface of dynamics, geometry, and number theory.
J.-C. Yoccoz -- Interval exchange maps and translation surfaces
A. Eskin -- Unipotent flows and applications
D. Kleinbock -- Quantitative nondivergence and its Diophantine applications
M. Einsiedler and E. Lindenstrauss -- Diagonal actions on locally homogeneous spaces
S. Katok -- Fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics
A. Avila -- Chaoticity of the Teichmuller flow
H. Oh -- Orbital counting via mixing and unipotent flows
G. Harcos -- Equidistribution on the modular surface and L-functions
N. Anantharaman -- Eigenfunctions of the Laplacian on negatively curved manifolds: A semiclassical approach
AMS/IP Studies in Advanced Mathematics, Volume: 48
2010; 381 pp; softcover
ISBN-13: 978-0-8218-5021-3
Expected publication date is September 22, 2010.
This volume represents selected proceedings of the Fourth International Congress of Chinese Mathematicians, held in Hangzhou, China. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Approximately fifteen hundred mathematicians participated in the Congress.
Graduate students and research mathematicians interested in many areas of mathematics.
Morningside lectures
J. Coates -- Number theory, ancient and modern
C. Procesi -- Partition functions and box-spline
C. Voisin -- Cohomology algebras in symplectic, Kahler and algebraic geometry
Plenary lectures
R. Bhatia -- Calculus of operator functions
I. Biswas -- Torelli for some moduli spaces
Z. Chen and X. Wu -- The adaptive PML method for acoustic wave scattering problems
A. Futaki -- Toric Sasaki-Einstein geometry
L. Ji -- Arithmetic groups, mapping class groups, related groups, and their associated spaces
D. Jiang -- On some topics in automorphic representations
F. Luo -- Rigidity of polyhedral surfaces
T. Mabuchi -- An affine sphere equation associated to Einstein toric surfaces
G. Prasad and A.S. Rapinchuk -- Number-theoretic techniques in the theory of Lie groups and differential geometry
R. Sujatha -- Local-global principles
R. G. Swan -- The flabby class group of a finite cyclic group
J. Xiao and F. Xu -- Green's formula in Hall algebras and cluster algebras
X.-P. Zhu -- The Ricci flow and geometrization of three-manifolds
Three lectures by Chinese women mathematicians
F. Chung -- Four proofs for the Cheeger inequality and graph partition algorithms
W.-C. W. Li -- Zeta functions in combinatorics and number theory
C.-L. Terng -- Soliton hierarchies constructed from involutions
Pure and Applied Undergraduate Texts, Volume: 11
2010; approx. 264 pp; hardcover
ISBN-13: 978-0-8218-5074-9
Expected publication date is November 17, 2010.
Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems and come equipped with hints when needed. Appropriate for both self-study and the classroom, the material is efficiently arranged so that milestones such as the Sylow theorems and Galois theory can be reached in one semester.
Undergraduate students interested in abstract algebra/modern algebra.
Arithmetic
Groups
Rings
Field theory
Index
Mathematical Surveys and Monographs, Volume: 165
2010; approx. 264 pp; hardcover
ISBN-13: 978-0-8218-5230-9
Expected publication date is October 17, 2010.
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content.
This book presents recent results on nonlocal evolution equations with
different boundary conditions, starting with the linear theory and moving
to nonlinear cases, including two nonlocal models for the evolution of
sandpiles. Both existence and uniqueness of solutions are considered, as
well as their asymptotic behaviour. Moreover, the authors present results
concerning limits of solutions of the nonlocal equations as a rescaling
parameter tends to zero. With these limit procedures the most frequently
used diffusion models are recovered: the heat equation, the p-Laplacian
evolution equation, the porous media equation, the total variation flow,
a convection-diffusion equation and the local models for the evolution
of sandpiles due to Aronsson-Evans-Wu and Prigozhin.
Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers.
The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.
Graduate students and research mathematicians interested in diffusion problems and nonlinear PDE.
The Cauchy problem for linear nonlocal diffusion
The Dirichlet problem for linear nonlocal diffusion
The Neumann problem for linear nonlocal diffusion
A nonlocal convection diffusion problem
The Neumann problem for a nonlocal nonlinear diffusion equation
Nonlocal p-Laplacian evolution problems
The nonlocal total variation flow
Nonlocal models for sandpiles
Nonlinear semigroups
Bibliography
Index