Formality of the complements of subspace arrangements with geometric lattices.
We derive new upper bounds for the densities of measurable sets in which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions . This gives new lower bounds for the measurable chromatic number in dimensions . We apply it to get a short proof of a variant of a recent result of Bukh which in turn generalizes theorems of Furstenberg,...