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.

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.

The European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' unites leading schools in analysis in Europe. In many cases, mathematical predictional power continues to make progress while the physical basis (in particular that of experimental physics) runs out power, due to natural engineering, technological and economical limitations. On the other hand, the fundamental mathematical understanding has to be modernized and updated. Complex and potential analysis in a broad sense has proved to be one of the most useful fields for providing a theoretical basis for mathematical physics. Includes supplementary material: sn.pub/extras

GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com