# Recent advances in geometric discrepancy

Josef Dick

UNSW

## Date:

Wed, 07/10/2015 - 2:30pm

## Venue:

K-J17-101 (Ainsworth Building 101) UNSW

## Abstract:

Classical discrepancy theory deals with distributing $N$ points in the $s$-dimensional unit cube as evenly as possible. The discrepancy function of the point set measures the deviation of the empirical measure from the uniform measure with respect to rectangular boxes anchored at the origin, and the $L^p$ discrepancy is the $L^p$ norm of the discrepancy function. While explicit constructions of point sets with asymptotically optimal $L^p$ discrepancy are known for $1<p<\infty$, much less is known about the $L^\infty$ discrepancy. In this talk we describe recent advances in the study of the bounded mean oscillation and exponential Orlicz norm of the discrepancy function.