| RUS ENG |
| Full version |
|
|
|
| SEMINARS |
|
Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
|
|||
|
|
|||
|
A review of the Schottky model of Riemann surfaces A. B. Bogatyrevabcd a Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow b Moscow Center for Fundamental and Applied Mathematics c Lomonosov Moscow State University d National Research University Higher School of Economics, Moscow |
|||
|
Abstract: The Schottky uniformization of Riemann surfaces has been used for efficient computations with surfaces and their moduli since the late 1980s. A review of this model and related computational algorithms will be given. For efficient solution of various equations in moduli spaces, we need explicit formulae that relate variations of function theoretic objects, such as Abelian integrals, with variations of group generators. These formulas were proposed by the author in 1997, and their computer implementation is based on another remarkable formula, invented by D. Hejhal back in the mid-1970s. |
|||