Efficient variational formulae for Schottky model of Riemann surfaces

Schottky uniformization of Riemann surfaces is used for the efficient calculations with surfaces and their moduli since the end of 1980-ies. I will talk of the the variational formulae which allow to efficiently compute the derivatives of various function theoretic objects (like abelian integrals and their periods) with respect to Schottky model. This allows to efficiently solve various equations in the moduli spaces.