Contemporary Mathematics, Volume: 562
2012; 297 pp; softcover
ISBN-13: 978-0-8218-5297-2
This volume contains the proceedings of the conference "New Trends in Noncommutative Algebra", held at the University of Washington, Seattle, in August 2010, in honor of Ken Goodearl's 65th birthday.
The articles reflect the wide interests of Goodearl and will provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Calabi-Yau algebras, quantum algebras and deformation quantization, Poisson algebras, growth of algebras, group algebras, and noncommutative Iwasawa algebras.
Graduate students and research mathematicians interested in noncommutative algebra, noncommutative algebraic geometry, and Lie algebras.
AMS/IP Studies in Advanced Mathematics, Volume: 51
2012; 999 pp; softcover
ISBN-13: 978-0-8218-7555-1
Expected publication date is March 31, 2012.
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
Research mathematicians interested in various topics.
Part 1
B. Andrews -- Gradient and oscillation estimates and their applications in geometric PDE
J. A. Chen and M. Chen -- On canonical and explicit classification of algebraic threefolds
C.-Y. Chi -- Canonical pseudonorms on pluricanonical spaces
J. Coates -- The enigmatic Tate-Shafarevich group
X. Dai -- Eta invariants for even dimensional manifolds
F. Fang and Z. Zhang -- Ricci flow on 4-manifolds and Seiberg-witten equations
L. Fargues and J.-M. Fontaine -- Vector bundles and p-adic Galois representations
B. Fu -- Geometry of nilpotent orbits: Results and conjectures
L. Fu -- Integrable connections and Galois representations
A. Futaki -- Asymptotic Chow polystability in Kahler geometry
W. T. Gan -- Representations of metaplectic groups
C. Fang and X. He -- Notes on partial conjugation
K.-W. Lan -- Geometric modular forms and the cohomology of torsion automorphic sheaves
N. C. Leung -- SYZ transformations for toric varieties
B. Guo and H. Li -- Some variational problems in conformal geometry
T. Draghici, T.-J. Li, and W. Zhang -- Geometry of tamed almost complex structures on 4-dimensional manifolds
W.-C. W. Li -- The arithmetic of noncongruence modular forms
Y.-P. Lee, H.-W. Lin, and C.-L. Wang -- Analytic continuations of quantum cohomology
K. Liu and P. Peng -- Mathematical aspects of string duality
X. Guo and H. Qin -- The tame kernels of number fields
B. Sun -- Notes on MVW-extensions
F. Chen and S. Tan -- Vertex operator representations for a class of BC_v-graded Lie algebras
H.-H. Tseng -- Notes on orbifold Gromov-Witten theory
L.-S. Tseng -- Cohomologies and elliptic operators on symplectic manifolds
M.-T. Wang -- Quasilocal mass from a mathematical perspective
S. Wang -- On dimension data, local VS global conjugacy
X.-J. Wang and B. Zhou -- Variational problems of Monge-Ampere type
S. Wu -- Wellposedness of the two and three dimensional full water wave problem
H.-W. Xu -- Recent developments in differentiable sphere theorems
R. Du and S. Yau -- New invariants for complex manifolds, singularities, and CR manifolds with applications
W. Zhang -- Gross-Zagier formula and arithmetic fundamental lemma
J. Zhou -- Integrality properties of mirror maps
X-Y. Zhou and L. Zhu -- Ohsawa-Takegoshi L^2 extension theorem: Revisited
Part 2
B.-L. Chen -- Regularity of Einstein spacetimes
K.-C. Chen -- A survey on retrograde and prograde orbits of the three-body problem by variational methods
D. X. Gu, W. Zeng, L. M. Lui, F. Luo, and S.-T. Yau -- Recent development of computational conformal geometry
B.-Y. Guo, C. Zhang, and T. Sun -- Some developments in spectral methods
L.-H. Huang -- On the center of mass in general relativity
Z. Huang -- Tailored finite point method for numerical simulation of partial differential equations
T. Lam -- Loop symmetric functions and factorizing matrix polynomials
A. Laptev -- Spectral inequalities for partial differential equations and their applications
E. K-W. Chu, T.-S. Huang, and W.-W. Lin -- Structured doubling algorithms for solving g-palindromic quadratic eigenvalue problems
Y. Lin -- Ricci curvature and functional inequalities on graphs
P. Lu -- Complexity dichotomies of counting problems
L. M. Lui, T. W. Wong, W. Zeng, X. Gu, P. M. Thompson, T. F. Chan, and S.-T. Yau -- A survey on recent development in computational quasi-conformal geometry and its applications
T. Luo -- Dynamics of shock fronts for some hyperbolic systems
L. Han and J.-S. Pang -- Time-stepping methods for linear complementarity systems
C.-W. Shu -- A brief survey on high order accurate maximum principle satisfying and positivity preserving discontinuous Galerkin and finite volume schemes for conservation laws
J. Smoller and B. Temple -- A one parameter family of expanding wave solutions of the Einstein equations that induces an anomalous acceleration into the standard model of cosmology
G. Strang -- Banded matrices with banded inverses and A-LPU
G. Wahba -- Dissimilarity data in statistical model building and machine learning
R.-H. Wang -- Some progress on computational geometry
J. Wei -- Geometrization program of semilinear elliptic equations
Z. Zhu, A. M.-C. So, and Y. Ye -- Fast and near-optimal matrix completion via randomized basis pursuit
J. Yin -- Mathematical questions of quantum dilute gases
X. Yuan -- Algebraic dynamics, canonical heights and Arakelov geometry
B.-Y. Zhang -- Well-posedness and control of the Korteweg-de Vries equation on a bounded domain
Y. Jiang, H. Zhang, and W. Zhu -- Statistical analysis in genetic association studies of mental illnesses
H. Zhao -- Compressible Navier-Stokes equations with large density oscillation
W. Zou -- Some results on variational and topological methods
Courant Lecture Notes, Volume: 23
2011; 111 pp; softcover
ISBN-13: 978-0-8218-7556-8
Expected publication date is March 16, 2012.
Any organism, to survive, must use a variety of defense mechanisms. A relatively recent evolutionary development is that of the adaptive immune system, carried to a quite sophisticated level by mammals. The complexity of this system calls for its encapsulation by mathematical models, and this book aims at the associated description and analysis. In the process, it introduces tools that should be in the armory of any current or aspiring applied mathematician, in the context of, arguably, the most effective system nature has devised to protect an organism from its manifold invisible enemies.
Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Graduate students and research mathematicians interested in immunology.
Pure and Applied Undergraduate Texts, Volume: 17
2012; approx. 388 pp; hardcover
ISBN-13: 978-0-8218-6932-1
Expected publication date is April 19, 2012.
This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration.
Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities.
This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits.
Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
Undergraduates and research mathematicians interested in analysis, number theory, and special functions.
Basic principles
Special sequences
Power series and related topics
Inequalities
Infinite products
Approximation by polynomials
Tauberian theorems
Fourier series
The gamma function
Two topics in number theory
Bernoulli numbers
The Cantor set
Differential equations
Elliptic integrals
Index
Graduate Studies in Mathematics, Volume: 133
2012; approx. 373 pp; hardcover
ISBN-13: 978-0-8218-7291-8
Expected publication date is April 14, 2012.
This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed.
Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations.
One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader.
The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.
Graduate students and research mathematicians interested in partial differential equations.
Simple examples of propagation
The linear Cauchy problem
Dispersive behavior
Linear elliptic geometric optics
Linear hyperbolic geometric optics
The nonlinear Cauchy problem
One phase nonlinear geometric optics
Stability for one phase nonlinear geometric optics
Resonant interaction and quasilinear systems
Examples of resonance in one dimensional space
Dense oscillations for the compressible Euler equations
Bibliography
Index