Main research activities of this institute are real and complex analysis, especially asymptotic analysis, special functions and applications to differential equations, functional equations and to the average case analysis of combinatorial algorithms. Furthermore, the team works on problems in analytic, probabilistic, and algorithmic number theory with applications to the effective solution of diophantine equations, to quasi-Monte Carlo methods and their application to special problems in finance and insurance. Finally, questions in general topology and ergodic theory are studied.