From Diff (S 1) to Univalent Functions. Cases of Degeneracy -- Poincaré—Steklov Integral Equations and Moduli of Pants -- Generalized Hamilton—Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups -- Bergen Lecture on -Neumann Problem -- Numerical Scheme for Laplacian Growth Models Based on the Helmholtz—Kirchhoff Method -- Gravitational Lensing by Elliptical Galaxies, and the Schwarz Function -- Nevanlinna Domains in Problems of Polyanalytic Polynomial Approximation -- Potential Theory in Denjoy Domains -- Carathéodory Convergence of Immediate Basins of Attraction to a Siegel Disk -- Rings and Lipschitz Continuity of Quasiconformal Mappings -- A Theoretical Algorithm to get a Schottky Uniformization from a Fuchsian one -- Scattering from Sparse Potentials: a Deterministic Approach -- Application of ATS in a Quantum-optical Model -- Geometry of Carnot-Carathéodory Spaces, Differentiability, Coarea and Area Formulas -- Fourier Transforms of UD Integrals -- Fredholm Eigenvalues of Jordan Curves: Geometric, Variational and Computational Aspects -- A Note on Life-span of Classical Solutions to the Hele—Shaw Problem -- The Fourier Transforms of General Monotone Functions -- Traces of Hörmander Algebras on Discrete Sequences -- Resonance Dynamics and Decoherence -- Ramified Integrals, Casselman Phenomenon, and Holomorphic Continuations of Group Representations -- The Stability of Solitary Waves of Depression -- Singular and Tangent Slit Solutions to the Löwner Equation -- A Remark on Amoebas in Higher Codimensions -- Quadratic Differentials and Weighted Graphs on Compact Surfaces -- Riesz Transforms and Rectifiability.

Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.