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,...
We show that every complete intersection defined by Laurent polynomials in an algebraic torus is isomorphic to a complete intersection defined by master functions in the complement of a hyperplane arrangement, and vice versa. We call systems defining such isomorphic schemes Gale dual systems because the exponents of the monomials in the polynomials annihilate the weights of the master functions. We use Gale duality to give a Kouchnirenko theorem for the number of solutions to a system of master...