edited by Stancho Dimiev (Bulgarian Academy of Sciences, Bulgaria)
& Kouei Sekigawa (Niigata University, Japan)

CONTEMPORARY ASPECTS OF COMPLEX ANALYSIS, DIFFERENTIAL GEOMETRY AND MATHEMATICAL PHYSICS
Proceedings of the 7th International Workshop on Complex Structures and Vector Fields
Plovdiv, Bulgaria 31 August - 4 September 2004

This volume presents the cutting-edge contributions to the Seventh International Workshop on Complex Structures and Vector Fields, which was organized as a continuation of the high successful preceding workshops on similar research.
The volume includes works treating ambitious topics in differential geometry, mathematical physics and technology such as Bezier curves in space forms, potential and catastrophy of a soap film, computer-assisted studies of logistic maps, and robotics.

Contents:

Readership: Researchers in analysis, differential geometry and mathematical physics.

360pp Pub. date: Jul 2005
ISBN 981-256-390-3

Yuval Z Flicker (The Ohio State University, USA)

AUTOMORPHIC FORMS AND SHIMURA VARIETIES OF PGSp(2)

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings.” This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,C) in SL(4, C). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum.
Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations.

To put these results in a general context, the book concludes with a technical introduction to Langlands’ program in the area of automorphic representations. It includes a proof of known cases of Artin’s conjecture.

Contents:

Readership: Graduate students and researchers in number theory, algebra and representation theory.

340pp Pub. date: Aug 2005
ISBN 981-256-403-9

edited by Juan M Maldacena (Institute for Advanced Study, USA)

PROGRESS IN STRING THEORY
TASI 2003 Lecture Notes, Boulder, Colorado, USA 2 - 27 June 2003

Intended mainly for advanced graduate students in theoretical physics, this comprehensive volume covers recent advances in string theory and field theory dualities. It is based on the annual lectures given at the School of the Theoretical Advanced Study Institute (2003) a traditional event that brings together graduate students in high energy physics for an intensive course given by leaders in their fields.
The first lecture by Paul Aspinwall is a description of branes in Calabi?Yau manifolds, which includes an introduction to the modern ideas of derived categories and their relation to D-branes. Juan Maldacena’s second lecture is a short introduction to the AdS/CFT correspondence with a short discussion on its plane wave limit. Tachyon condensation for open strings is discussed in the third lecture by Ashoke Sen while Eva Silverstein provides a useful summary of the various attempts to produce four-dimensional physics out of string theory and M-theory in the fourth lecture. Matthew Strassler’s fifth lecture is a careful discussion of a theory that has played a very important role in recent developments in string theory ? a quantum field theory that produces a duality cascade which also has a large N gravity description. The sixth lecture by Washington Taylor explains how to perform perturbative computations using string field theory.

The written presentation of these lectures is detailed yet straightforward, and they will be of great use to both students and experienced researchers in high energy theoretical physics.

Contents:

Readership: Graduates, academics and researchers in high energy, particle, theoretical and mathematical physics.

572pp Pub. date: Jul 2005
ISBN 981-256-406-3

Simeon Reich (The Technion Israel Institute of Technology, Israel)
& David Shoikhet (ORT Braude College, Israel)

NONLINEAR SEMIGROUPS, FIXED POINTS, AND GEOMETRY OF DOMAINS IN BANACH SPACES

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.
Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments.

Contents:

Readership: Upper-level undergraduates, graduate students, and researchers.

372pp Pub. date: Jul 2005
ISBN 1-86094-575-9