Discrepancy theory deals with point distribution in compact spaces, measuring the
discrepancy between empirical distribution and target distribution. Most prominent
are the star-discrepancy problem, asking for the optimal rate of convergence of the
supremum of the discrepancy function, and the inverse of the star-discrepancy problem,
asking for explicit constructions of point sets whose discrepancy depends at most
polynomially on the dimension. The first problem is related to quasi-Monte Carlo
integration, whereas the second problem seems more closely related to pseudo-random
number generators. Point distributions on the unit sphere and point distributions
with respect to non-uniform target measures are also of great interest.
A tutorial giving an introduction to some of the main topics of the workshop will be given by Dmitriy Bilyk:
"Uniform Distribution and Discrepancy Theory: At the crossroads of analysis, approximation, discrete geometry,
number theory, probability, and more..."