Discrepancy theory and quasi-Monte Carlo methods
Tractablity of high dimensional problems
Two lecture series:
- Tutorial I
Christoph Aistleitner (TU Graz)
Uniform distribution and discrepancy: Analytic, number-theoretic and computational aspects
19.-21. September 2017, jeweils 10:15-11:45
This course starts with a basic introduction to the classical theory of uniform distribution modulo one and to discrepancy theory. We describe how the subject evolved since the beginning of the twentieth century, and recall several classical results (first day). We describe the connection with Fourier analysis, give a proof of the Erdös-Turan inequality and of Koksma’s inequality, and show some applications in number theory (second day). We recall basic facts of Quasi-Monte Carlo integration, present the viewpoint of tractability theory, and prove upper and lower bounds for the inverse of the discrepancy. For this purpose we introduce tools from non-parametric statistics, combinatorial complexity theory and metric entropy theory (third day).
2. Tutorial II
Henryk Wozniakowski (Columbia University, New York, and University of Warsaw)
ABC on IBC and Tractability
2.-6. Oktober 2017, jeweils 10:00-11:00
I plan to cover basic issues of IBC=Information-Based Complexity and then discuss various notions of tractability of multivariate problems. No prior knowledge of the subject is required.