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In the past decade, the mathematics of superconductivity has been the subject of intense study. This book examines in detail the nonlinear Ginzburg-Landau (GL) functional, the model most commonly used. Specifically, cases in the presence of a strong magnetic field and with a sufficiently large GL parameter kappa are covered.

Key topics and features:

*Provides a concrete introduction to techniques in spectral theory and PDEs

*Offers a complete analysis of the two-dimensional GL-functional with large kappa in the presence of a magnetic field

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The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, thus providing the complex analysis backbone of Loewner theory. The new materials found in this edition give a concise and accessible treatment of Loewner theory. Some of them have been described in research papers only or appear here for the first time. Each chapter finishes with exercises.

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, thus providing the complex analysis backbone of Loewner theory. The new materials found in this edition give a concise and accessible treatment of Loewner theory. Some of them have been described in research papers only or appear here for the first time. Each chapter finishes with exercises.