A publication of the Theta Foundation.
2008; 148 pp; hardcover
ISBN-13: 978-973-87899-1-3
The volume represents the proceedings of the conference "Operator Algebras and Mathematical Physics 3", held in Bucharest, Romania, in August 2005. It contains eight refereed papers on the following topics:
holomorphic representations of Jacobi algebras
groupoid C^*-algebras
the reduced C^*-algebra of the Thompson group F
classical low-energy scattering for a two-body system
compact quantum groups
Schrodinger operators and the Fermi golden rule
boundary topological invariants in some physical systems
index and homology of pseudodifferential operators on manifolds with boundary
A publication of the Theta Foundation. Distributed worldwide, except in Romania, by the AMS.
Graduate students and research mathematicians interested in analysis.
S. Berceanu -- A holomorphic representation of the multidimensional Jacobi algebra
M. R. Buneci -- Groupoid categories
I. Chifan and G. Picioroag? -- C^*-estimates for averaging sums of elements
in the Thompson group F
J. Derezi?ski and E. Skibsted -- Classical scattering at low energies
R. Dumitru -- Unitary representations of compact quantum groups
A. Jensen and G. Nenciu -- On the Fermi golden rule: degenerate eigenvalues
J. Kellendonk and S. Richard -- Topological boundary maps in physics
S. Moroianu and V. Nistor -- Index and homology of pseudodifferential operators on manifolds with boundary
A publication of the Theta Foundation.
2008; 229 pp; hardcover
ISBN-10: 973-87899-2-3
ISBN-13: 978-973-87899-2-0
The volume represents the proceedings of the 21st International Conference on Operator Theory, held in Timisoara, Romania, in 2006. Three of the included papers are surveys on active areas of research:
renormalization group in algebraic quantum field theory
composition operators on Hardy-Orlicz and Banach-Orlicz spaces
operator ideals on Hilbert spaces
The remaining fourteen papers contain original research on a wide variety of topics:
single operator theory
Banach algebras
C^*-algebras
von Neumann algebras
Hilbert and Banach modules
differential and integral operators
noncommutative probability
spectral theory
Graduate students and research mathematicians interested in analysis.
A. M. Bikchentaev -- Local convergence in measure on semifinite algebras. III
I. Biswas, G. Misra, and C. Varughese -- Geometric invariants from the resolution for the quotient module along a multi-dimensional grid
M. R. Buneci -- Borel morphisms and C^*-algebras
G. Cassier and L. Suciu -- Mapping theorems and similarity to contractions
for classes of A-contractions
A. Colojoar? -- Symmetric algebra ofmathcal{L}(X,F) as an algebra of polynomials
R. Conti, C. D'Antoni, and G. Morsella -- Renormalization group in algebraic quantum field theory: past, present and future
R. G. Douglas -- Essentially reductive Hilbert modules. II
M. Joi?a -- Countably generated Hilbert modules, multiplier modules, and
stable isomorphisms of locally C^*-algebras
V. Kaftal and G. Weiss -- A survey on the interplay between arithmetic mean ideals, traces, lattices of operator ideals,and an infinite Schur-Horn majorization theorem
L. D. Lemle -- L^infty-uniqueness of Schrodinger operators restricted in
an open domain
M. Megan and L. Buliga -- Nonuniform exponential trichotomy for linear difference equations in Banach spaces
M. Megan and C. Stoica -- Equivalent definitions for uniform exponential trichotomy of evolution operators in Banach spaces
H. Queffelec -- Composition operators on Hardy-Orlicz and Bergman-Orlicz spaces of the disk
F. R?dulescu -- The von Neumann algebra of the non-residually finite Baumslag
group langle a,b|ab^{3}a^{-1}=b^{2} rangle embeds into R^{omega}
S. M. Stoian -- Spectral properties for locally bounded operators
L. Suciu -- Block representation for A-contractions
L. Zielinski -- Eigenvalue asymptotics for a class of Jacobi matrices
Courant Lecture Notes, Volume: 17
2008; 197 pp; softcover
ISBN-13: 978-0-8218-4701-5
This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrodinger equations," which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrodinger-type equations.
At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic.
Graduate students and research mathematicians interested in PDE's of Schrodinger and kinetic type.
Fields Institute Communications, Volume: 53
2008; 395 pp; hardcover
ISBN-13: 978-0-8218-4275-1
The papers collected in this volume reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems.
While dynamics of polynomial mappings, particularly quadratics, has by now reached a mature state of development, much less is known about non-polynomial rational maps. The reader will be introduced into this fascinating world and a related area of transcendental dynamics by the papers in this volume. A graduate student will find an area rich with open problems and beautiful computer simulations.
A survey by V. Nekrashevych introduces the reader to iterated monodromy groups of rational mappings, a recently developed subject that links geometric group theory to combinatorics of rational maps. In this new language, many questions related to Thurston's theory of branched coverings of the sphere can be answered explicitly.
Renormalization theory occupies a central place in modern Complex Dynamics. The progress in understanding the structure of the Mandelbrot set, polynomial Julia sets, and Feigenbaum-type universalities stems from renormalization techniques. Renormalization of circle maps and rotation domains, such as Siegel disks, can be understood in the context of the classical KAM theory. Corresponding phenomena in higher dimensions, such as universal scaling in area-preserving maps in 2D, on the boundary of KAM, pose a challenging problem. A survey by H. Koch and several other papers in the volume will introduce the reader to this direction of study.
Graduate students and research mathematicians interested in complex dynamical systems and renormalization in dynamics.
Fields Institute Communications, Volume: 54
2008; 297 pp; hardcover
ISBN-13: 978-0-8218-4484-7
Modular forms have long played a key role in the theory of numbers, including most famously the proof of Fermat's Last Theorem. Through its quest to unify the spectacularly successful theories of quantum mechanics and general relativity, string theory has long suggested deep connections between branches of mathematics such as topology, geometry, representation theory, and combinatorics. Less well-known are the emerging connections between string theory and number theory. This was indeed the subject of the workshop Modular Forms and String Duality held at the Banff International Research Station (BIRS), June 3-8, 2006. Mathematicians and physicists alike converged on the Banff Station for a week of both introductory lectures, designed to educate one another in relevant aspects of their subjects, and research talks at the cutting edge of this rapidly growing field.
This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory.
The book is suitable for researchers working at the interface of number theory and string theory.
Readership
Graduate students and research mathematicians interested in number theory and physics.