Let F be a finite subset of ℤd. We say that F is a translational tile of ℤd if it is possible to cover ℤd by translates of F with no overlaps. Given a finite subset F of ℤd, could we determine whether F is a translational tile in finite time? Suppose that F does tile, does it admit a periodic tiling? A well known argument of Wang shows that these two questions are closely related. In the talk, we will discuss this relation and present some new results, joint with Terence Tao, on the rigidity of tiling structures in ℤ2, and their applications to decidability.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
