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Seminar on Complex Analysis (Gonchar Seminar)
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Schottky Model: An Efficient Computational Tool A. B. Bogatyrev Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow |
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Abstract: The Schottky uniformization of Riemann surfaces (with incomplete dissection) has been used for efficient computations with surfaces and their moduli since the late 1980s. We provide an overview of this model and related computational algorithms. For solving equations for surface moduli, explicit formulas that relate variations of function theory objects (e.g., Abelian integrals or their periods) to variations of group generators are proposed. These formulas become numerically efficient with the use of D. Heijal's formulas, invented around 1975. Website: https://zoom.us/j/7743848073?pwd=QnJmZjQ5OEV1c3pjenBhcUMwWW9XUT09 * ID: 774 384 8073. Password: L8WVCc |
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