Ian H. Sloan School of Mathematics and Statistics University of New South Wales Location: Carslaw 173 Time: 2pm Friday, March 11, 2011 Title: The challenge of high-dimensional computation Abstract: Richard Bellman coined the phrase the curse of dimensionality to describe the extraordinarily rapid increase in the difficulty of typical problems as the number of variables increases. A typical problem is numerical multiple integration, where it is clear that the cost of every integration formula of product type rises exponentially with the number of dimensions. Nevertheless, problems with hundreds or even thousands of variables do arise, and are now being tackled successfully. In this talk I will touch briefly on recent advances in understanding and constructing high dimensional integration rules, but much of the focus will be on applications, in mathematical finance, linear models in statistics, and flow through random porous media. A common theme is that high-dimensional problems present a major challenge for contemporary computation.