High Dimensional Integration -- From Information-Based Complexity to Uncertainty Quantification


Ian Sloan


Richard Bellman coined the phrase “the curse of dimensionality” to describe the extraordinarily rapid increase in the difficulty of many problems as the number of variables increases. Yet in 1995 Paskov and Traub successfully computed 360-dimensional integrals for a problem in finance. In this talk I will show how advances spurred by that discovery have led to applications in “uncertainty quantification”, typified by the flow of a fluid through a porous medium with random permeability.