CRM Proceedings & Lecture Notes, Volume: 56
2013; approx. 228 pp; softcover
ISBN-13: 978-0-8218-9418-7
Expected publication date is February 27, 2013.
This book contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieures in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation. In recent decades, metric measure spaces have emerged as a fruitful source of mathematical questions in their own right, and as indispensable tools for addressing classical problems in geometry, topology, dynamical systems, and partial differential equations. The summer school was designed to lead young scientists to the research frontier concerning the analysis and geometry of metric measure spaces, by exposing them to a series of minicourses featuring leading researchers who highlighted both the state-of-the-art and some of the exciting challenges which remain.
This volume attempts to capture the excitement of the summer school itself, presenting the reader with glimpses into this active area of research and its connections with other branches of contemporary mathematics.
Graduate students and research mathematicians interested in metric measure spaces and optimal transportation.
L. Ambrosio -- An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below
M. T. Barlow -- Analysis on the Sierpinski carpet
T. Coulhon -- Heat kernel estimates, Sobolev-type inequalities and Riesz transform on noncompact Riemannian manifolds
G. David -- Regularity of minimal and almost minimal sets and cones: J. Taylor's theorem for beginners
Y.-H. Kim -- Lectures on Ma-Trudinger-Wang curvature and regularity of optimal transport maps
R. J. McCann and N. Guillen -- Five lectures on optimal transportation: Geometry, regularity and applications
E. Milman -- A proof of Bobkov's spectral bound for convex domains via Gaussian fitting and free energy estimation
Y. Ollivier -- A visual introduction to Riemannian curvatures and some discrete generalizations
Contemporary Mathematics, Volume: 585
2013; approx. 334 pp; softcover
ISBN-13: 978-0-8218-7564-3
Expected publication date is February 28, 2013.
This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4-8, 2011, at the University of Almeria, Almeria, Spain.
The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects on the classification of fusion categories using Morita equivalence methods, a long comprehensive introduction to Hopf algebras in the category of species, a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other topics discussed in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, relations to the conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.
Graduate students and research mathematicians interested in Hopf algebra theory, tensor categories, quantum groups, representation theory, and combinatorics and conformal field theory.
A. L. Agore and G. Militaru -- Unified products and split extensions of Hopf algebras
M. Aguiar and S. Mahajan -- Hopf monoids in the category of species
M. Beattie and G. A. Garcia -- Classifying Hopf algebras of a given dimension
G. Bohm and J. Gomez-Torrecillas -- On the double crossed product of weak Hopf algebras
A. Bruguieres and A. Virelizier -- The doubles of a braided Hopf algebra
G. Carnovale -- Induced conjugacy classes and induced UƒÃ(G)-modules
M. Cohen and S. Westreich -- Recovering information from character tables of Hopf algebras: Normality, dimensions and quotients
M. Elhamdadi and A. Makhlouf -- Hom-quasi-bialgebras
F. Fantino and L. Vendramin -- On twisted conjugacy classes of type D in sporadic simple groups
J. M. F. Vilaboa, R. G. Rodriguez, and A. B. R. Raposo -- Partial and unified crossed products are weak crossed products
L. Li and Y. Zhang -- The Green rings of the generalized Taft Hopf algebras
D. Nikshych -- Morita equivalence methods in classification of fusion categories
Contemporary Mathematics, Volume: 587
2013; 243 pp; softcover
ISBN-13: 978-0-8218-8318-1
Expected publication date is February 23, 2013.
This volume contains the proceedings of the International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, held November 13-18, 2011, at the Banff International Research Station, Banff, Alberta, Canada.
The articles in this volume cover the arithmetic theory of quadratic forms and lattices, as well as the effective Diophantine analysis with height functions. Diophantine methods with the use of heights are usually based on geometry of numbers and ideas from lattice theory. The target of these methods often lies in the realm of quadratic forms theory. There are a variety of prominent research directions that lie at the intersection of these areas, a few of them presented in this volume:
Representation problems for quadratic forms and lattices over global fields and rings, including counting representations of bounded height.
Small zeros (with respect to height) of individual linear, quadratic, and cubic forms, originating in the work of Cassels and Siegel, and related Diophantine problems with the use of heights.
Hermite's constant, geometry of numbers, explicit reduction theory of definite and indefinite quadratic forms, and various generalizations.
Extremal lattice theory and spherical designs.
Graduate students and research mathematicians interested in number theory, in particular in Diophantine problems, quadratic forms, and lattices.
G. Nebe -- Boris Venkov's theory of lattices and spherical designs
J. M. Cervino and G. Hein -- Generalized theta series and spherical designs
W. K. Chan and B.-K. Oh -- Representations of integral quadratic polynomials
R. Coulangeon and G. Nebe -- Dense lattices as Hermitian tensor products
R. Dietmann -- Small zeros of homogeneous cubic congruences
A. G. Earnest and J. Y. Kim -- Strictly regular diagonal positive definite quaternary integral quadratic forms
L. Fukshansky -- Heights and quadratic forms: Cassels' theorem and its generalizations
J. J. A. Gonzalez and F. Luca -- On the positive integers n satisfying the equation Fn=x2+ny2
J. Hanke -- Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields
D. R. Heath-Brown -- p adic zeros of systems of quadratic forms
D. Kettlestrings and J. L. Thunder -- The number of function fields with given genus
G. T. Minton -- Unique factorization in the theory of quadratic forms
G. Nebe -- Golden lattices
R. Scharlau -- The extremal lattice of dimension 14, level 7 and its genus
A. Schurmann -- Strict periodic extreme lattices
C.L. Stewart -- Exceptional units and cyclic resultants, II
J. D. Vaaler and M. Widmer -- A note on generators of number fields
T. Watanabe, S. Yano, and T. Hayashi -- Voronoi's reduction theory of GLn over a totally real number field
M. Watkins -- Some comments about indefinite LLL
MSRI Mathematical Circles Library, Volume: 12
2013; 172 pp; softcover
ISBN-13: 978-0-8218-6905-5
Expected publication date is February 24, 2013.
Held annually in Moscow since 1990, the Mathematical Festival is a brilliant and fascinating math competition attended by hundreds of middle school students. Participants of the Festival solve interesting mathematical problems and partake in other engaging activities, while cultivating key skills such as intuitive reasoning and quick thinking. This book contains problems presented at the Festival during the years 1990-2011, along with hints and solutions for many of them. Most of the problems are accessible to students with no additional training in mathematics and may be used as supplementary material at school or at home. Other problems, however, are more advanced and will be enjoyed by students with a deeper interest in mathematics.
Most of the problems in this book are specially created for Mathematical Festival competitions by leading Russian experts in school and extracurricular math education and have never been published before.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Middle school students, their parents, and teachers.
Problems
Answers
Hints
Solutions
Thematic index
Contemporary Mathematics, Volume: 586
2013; 424 pp; softcover
ISBN-13: 978-0-8218-8737-0
Expected publication date is March 23, 2013.
The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs.
This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.
Graduate students and research mathematicians interested in scientific computing and its applications, science, and engineering.
S. Acosta, S.-S. Chow, and V. Villamizar -- Multifrequency inverse source problem for elastic waves
T. Arbogast, Z. Tao, and H. Xiao -- Multiscale mortar mixed methods for heterogeneous elliptic problems
R. E. Bank and H. Nguyen -- A parallel hp-adaptive finite element method
J. W. Banks, J. A. F. Hittinger, J. M. Connors, and C. S. Woodward -- A Posteriori error estimation via nonlinear error transport with application to shallow water
G. Bao, G. Hu, D. Liu, and S. Luo -- Multi-physical modeling and multi-scale computation of nano-optical responses
R. Basnayake, A. Luttman, and E. Bollt -- A lagged diffusivity method for computing total variation regularized fluid flow
J. Blair, E. Machorro, and A. Luttman -- Estimating the bias of local polynomial approximation methods using the Peano kernel
V. A. Bokil and N. L. Gibson -- Stability and dispersion analysis of high order FDTD methods for Maxwell's equations in dispersive media
A. L. Bowers -- Numerical approximation of a multiscale Leray model for incompressible, viscous flow
J. Cao and C. Xu -- A high order schema for the numerical solution of ordinary fractional differential equations
C. Chen and Q. Wang -- 3-D patterns in bacterial biofilms
J. Chen and Z. Wu -- Critical path for an optimal hedging strategy
Z. Chen, H. Liu, S. Yu, B. Hsieh, and L. Shao -- Reservoir simulation on NVIDIA Tesla GPUs
S. Congreve and P. Houston -- Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration
E. M. D'Agnillo and L. G. Rebholz -- On the enforcement of discrete mass conservation in incompressible flow simulations with continuous velocity approximation
H. Feng, A. Barua, X. Li, and S. Li -- An adaptive treecode algorithm for computing the evolution of microstructures in an elastic media
Z. Gu and Y. Chen -- Chebyshev spectral-collocation method for Volterra integral equations
W. Han, Y. Li, Q. Sheng, and J. Tang -- A numerical method for generalized Fokker-Planck equations
J. Howell, H. Lee, and S. Xu -- Numerical study of a viscoelastic flow in a moving domain
J. Huang, X. Huang, and S. Zhang -- A superconvergence of the Morley element via postprocessing
G. Jouvet, E. Bueler, C. Graser, and R. Kornhuber -- A nonsmooth Newton multigrid method for a hybrid, shallow model of marine ice sheets
M. G. Larson and F. Bengzon -- Component modal synthesis for laminar viscous incompressible fluid flow
W. Layton and A. Takhirov -- Numerical analysis of wall adapted nonlinear filter models of turbulent flow
H. Li and V. Nistor -- LNG-FEM: Graded meshes on domains of polygonal structures
J. Li and J. Waters -- Homogenized discontinuous Galerkin method for Maxwell's equations in periodic structured dispersive media
T. Lin, Y. Lin, and X. Zhang -- Immersed finite element method of lines for moving interface problems with nonhomogeneous flux jump
P. H. Muir -- B-spline Gaussian collocation software for 1D parabolic PDEs
R. D. Nair and K. K. Katta -- The central-upwind finite-volume method for atmospheric numerical modeling
M. Neda, F. Pahlevani, and W. Waters -- Sensitivity computations of the Leray-ƒ¿ model
Schiavazzi Schiavazzi, A. Doostan, and G. Iaccarino -- A sparse multiresolution stochastic approximation for uncertainty quantification
D. Schotzau and X. Wei -- A mixed finite element method for a time-dependent incompresible MHD problem
Q. Sheng and S. Guha -- A compact splitting scheme approach on nonuniform grids
C.-W. Shu -- Survey on discontinuous Galerkin methods for Hamilton-Jacobi equations
P. Song and I. Yotov -- Coupling surface and subsurface flows with curved interfaces
J. Sun and C. Zheng -- Reconstruction of obstacles embedded in waveguides
P. Sun, L. Zhang, C. Liu, and J. Xu -- Full Eulerian modeling and effective numerical studies for the dynamic fluid-structure interaction problem
S. Wang and Z. Li -- A multiple-endpoints Chebysheve collocation method for high order differential equations
A. Warzy?ski, M. E. Hubbard, and M. Ricchiuto -- Discontinuous residual distribution schemes for time-dependent problems
W. Layton, H. Tran, and C. Trenchea -- Stability of partitioned methods for magnetohydrodynamics flows at small magnetic Reynolds number
Tata Institute of Fundamental Research
2013; 550 pp; hardcover
ISBN-13: 978-93-80250-49-6
Expected publication date is April 6, 2013.
This volume contains the proceedings of the International Colloquium on Representations and L-functions organized by the Tata Institute of Fundamental Research in January 2012, one of a series of colloquia that began in 1956. It covers a wide spectrum of mathematics, including classifications of representations, arithmeticity, the average size of the 2-Selmer group of Jacobians for certain hyperelliptic curves, certain Kuznetsov formula for symmetry types of families of L-functions, sub-convexity bounds in the level aspect, Linnik's ergodic method, beyond endoscopy, and harmonic analysis for the relative trace formula.
This volume contains refereed articles by leading experts in these fields and includes original results as well as expository materials in these areas.
A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka.
Graduate students and research mathematicians interested in number theory.
J. Arthur -- The endoscopic classification of representations
M. Bhargava and B. D. Gross -- The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
P. Cho and H. Kim -- Weil's theorem on rational points over finite fields and Artin L-functions
W. T. Gan and A. Raghuram -- Arithmeticity for periods of automorphic forms
E. Ghate -- Control theorems for ordinary 2-adic families of modular forms
D. Goldfeld and A. Kontororich -- On the GL(3) Kuznetsov formula with applications to symmetry types of families of L-functions
R. Holowinsky and R. Munshi -- Level aspect sub-convexity for Rankin-Selberg L-functions
E. Lapid -- On the Harish-Chandra Schwartz space of G(F)?G(A)
S. T. Lee and C. Zhu -- Degenerate principal series of metaplectic groups and Howe correspondence
P. Michel, J. Ellenberg, and A. Venkatesh -- Linnik's ergodic method and distribution of integer points on spheres
R. Murty -- The Fibonacci Zeta-function
D. Ramakrishnan -- Decomposition and signs of l-adic representations attached to algebraic automorphic forms on GL(4)
D. Rohrlich -- Self-dual Artin representations
A. Saha -- Determination of modular forms by fundamental Fourier coefficients
Y. Sakellaridis -- Beyond endoscopy for the relative trace formula I : Local theory
M. Tadic -- On interactions between harmonic analysis and the theory of automorphic forms
E. Urban -- On the rank of Selmer groups of elliptic curves over Q
W. Zhang -- Harmonic analysis for relative trace formula