Wednesday, December 2, 2020
12/02/2020 - 4:15pm
Let F be a finite subset of the d-dimensional integer lattice. We say that F is a translational tile of Z^d if it is possible to cover Z^d by translates of F with no overlaps.
Given a finite subset F of Z^d, could we determine whether F is a translational tile in finite time? Suppose that F does tile, what can be said about the structure of the 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 Z^2, and their applications to decidability.