Lifting the curse of dimensionality: numerical integration in high dimensions

Richard Bellmann coined the phrase “the curse of dimensionality” to describe the extraordinarily rapid increase in the difficulty of most problems as the number of variables increases. A typical problem is numerical multiple integration, where the cost of any integration formula of product type obviously rises exponentially with the number of variables. Nevertheless, problems with hundreds or even thousands of variables do arise, and are now being tackled successfully. In this talk I will describe recent strategies, mathematical settings, and constructions with which suitable integration problems (from mathematical finance, for example) are being successfully handled.