It is well known that if a finite set of integers A tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A+B=ZM of a finite cyclic group. Coven and Meyerowitz (1998) proposed a characterization of all finite tiles in terms of the cyclotomic divisors of associated mask polynomials, and proved it when the tiling period M has at most two distinct prime factors. In joint work with Itay Londner, we extended it to the case when M=(pqr)2, where p,q,r are distinct primes. The methods we developed can be applied to other questions that hinge on cyclotomic divisibility, ranging from number theory to harmonic analysis and geometric measure theory. In particular, Caleb Marshall and I were able to use cyclotomic divisibility methods to prove new Favard length estimates for product Cantor sets. The talk will provide an introduction to this group of problems.
This video is part of the Webinar in Additive Combinatorics series, and this is
their YouTube channel.
