This volume presents the proceedings of the conference on "Trends in Mathematical Physics" held at the University of Tennessee. The conference drew international experts from mathematical and computational physics. The following topics were addressed: superstrings and quantum gravity, pattern formation, and crystallographic topology. The cutting-edge research reflected in the extensive surveys in the book are written for a diverse audience.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Graduate students, research mathematicians, and physicists interested in quantum theory.

Table of Contents

• R. R. Aldinger -- Berry's connection in a quantum relativistic description of the curved space analogue of development
• I. G. Avramidi and G. Esposito -- Heat-kernel asymptotics of the Gilkey-Smith boundary-value problem
• I. G. Avramidi and G. Esposito -- On ellipticity and gauge invariance in Euclidean quantum gravity
• A. L. Bertozzi, A. Münch, and M. Shearer -- Undercompressive waves in driven thin film flow: Theory, computation, and experiment
• A. V. Bogdanov, A. S. Gevorkyan, and A. G. Grigoryan -- Internal time peculiarities as a cause of bifurcations arising in classical trajectory problem and quantum chaos creation in three-body systems
• A. V. Bogdanov, A. S. Gevorkyan, and A. G. Grigoryan -- Random motion of quantum harmonic oscillator-Thermodynamics of nonrelativistic vacuum
• A. J. Bordner -- A new formulation of Lax pairs for generalized Calogero-Moser models
• G. Chalmers and K. Schalm -- Four-point correlation functions in the AdS/CFT correspondence
• S. A. Cherkis -- Gravitational instantons and moduli spaces
• E. Cremmer, B. Julia, H. Lü, and C. N. Pope -- Superdualities and twisted self-duality
• I. Dasgupta -- Boomerons in field theory
• M. J. Duff -- A layman's guide to $M$-theory
• J. K. Elwood -- Family symmetry, the anomalous $U(1)$, and neutrino mixing
• D. Ennyu, H. Kawabe, and N. Nakazawa -- Stochastic quantization approach to $c \leq 1$ open-closed string field theories
• C. D. Fosco -- Gauge invariance and effective actions at finite temperature
• I. Giannakis -- Superconformal deformations and space-time symmetries
• M. E. Glicksman -- Nonlinear patterns in microstructures
• C. R. Hagen -- Non-thermalizability of a quantum field theory
• R. A. Hefferlin -- Field theory for chemical spaces
• J. Hoppe -- From functions to matrices
• E. Horozov and A. Kasman -- Duality and construction of quantum integrable systems
• G. Huisken -- Geometric concepts for the mass in general relativity
• C. K. Johnson -- Crystallographic topology 2: Overview and work in progress
• I. I. Kogan and O. A. Soloviev -- Gravitationally dressed RG flows, zigzag symmetry and zero-tension strings
• C. LeBrun -- Einstein metrics and the Yamabe problem
• R. López-Alemán -- Numerical evolution in time of curvature perturbations in Kerr black holes
• A. Ludu and J. P. Draayer -- Nonlinearity and self-similarity: Wavelets and compactons on a physical background
• B. A. Magradze -- On analytic approach to perturbative quantum chromodynamics
• C. Michael -- Lattice gauge theory
• R. I. Nepomechie -- Integrable models with boundary
• H. Neuberger -- Mathematical aspects of chiral gauge theories on the lattice
• L. A. Pando Zayas -- The statistical entropy of black holes and the $AdS_3$ geometry
• E. M. Rabei -- Canonical treatment of regular Lagrangians with holonomic constraints as singular systems
• C. Rasinariu, U. P. Sukhatme, and A. Gangopadhyaya -- Algebraic shape invariant models
• W. Rivera-Gallego -- Molecular configurations and Euclidean distance matrices
• I. A. Shovkovy -- Derivative expansion of the one-loop effective action in QED
• C. H. Taubes -- Nonlinear generalizations of a 3-manifold's Dirac operator
• C.-L. Wu -- Dynamical symmetry approach to quantum many-body problems