Pattern equivariant cohomology and theorems of Kesten and Oren

Abstract

In 1966, Harry Kesten settled the Erdős–Szüsz conjecture on the local discrepancy of irrational rotations. His proof made heavy use of continued fractions and Diophantine analysis. In this paper, we give a purely topological proof Kesten's theorem (and Oren's generalization of it) using the pattern equivariant cohomology of aperiodic tiling spaces.