Computing with Riemann Surfaces

The theory of Riemann surfaces, which emerged as a field of analysis, has found numerous applications in other mathematical disciplines, as well as in mechanics, theoretical physics, engineering, etc. Many model problems admit exact solutions in terms of function-theoretical objects on Riemann surfaces or their moduli spaces (formulas of Matveev–Its, Zolotarev, etc.). The talk will consider the issues of efficient computation of objects like Abelian integrals, their periods, linear and quadratic differentials, meromorphic functions etc. for surfaces of higher ($> 1$) genus. Examples of solving different problems will be given.