CARMA COLLOQUIUM Speaker: Josef Dick, School of Mathematics and Statistics, University of NSW Title: High-dimensional Numerical Integration Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 16th Jun 2011 Abstract: High-dimensional integrals come up in a number of applications like statistics, physics and financial mathematics. If explicit solutions are not known, one has to resort to approximative methods. In this talk we will discuss equal-weight quadrature rules called quasi-Monte Carlo. These rules are defined over the unit cube $[0,1]^s$ with carefully chosen quadrature points. The quadrature points can be obtained using number-theoretic and algebraic methods and are designed to have low discrepancy, where discrepancy is a measure of how uniformly the quadrature points are distributed in $[0,1]^s$. In the one-dimensional case, the discrepancy coincides with the Kolmogorov-Smirnov distance between the uniform distribution and the empirical distribution of the quadrature points and has also been investigated in a paper by Weyl published in 1916. [Permanent link]