Dispersion and Diophantine Approximation [Please note the change of time]

The dispersion of a finite set, say, in [0, 1) is a quantitative measure of its denseness.
It is defined to be the largest gap between neighbouring elements. Recently, Sam Chow and me
discovered a link between dispersion and multiplicative Diophantine approximation. After a brief
introduction to multiplicative Diophantine approximation, I will discuss how this link allows us
to improve several results by, roughly, the square-root of a logarithm.