Computational approach to Riemann surfaces

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This volume provides a structured overview of computational approaches to Riemann surfaces, showcasing both existing methods and those in development. Contributions come from groups that offer publicly available numerical codes, illustrating the software tools accessible for practical use. It includes examples of solutions to partial differential equations and surface theory. The intended audience is twofold: it serves as a textbook for graduate courses in the numerics of Riemann surfaces, requiring only a standard undergraduate background in calculus and linear algebra, with no prior knowledge of Riemann surface theory needed, as the Introduction covers the essentials. Additionally, it caters to specialists in geometry and mathematical physics who utilize Riemann surfaces in their research. This book is the first to reflect the progress made in this field over the last decade, featuring original results. The increasing applications of Riemann surfaces in evaluating concrete characteristics of models are highlighted, with many problem settings and computations motivated by practical applications in geometry and mathematical physics.