András Biró: Periodicity of translational tilings in Z^2 (after Bhattacharya, Greenfeld and Tao)

Abstract:

If d is a positive integer and F is a finite subset of Z^d, a tiling of  Z^d by F is a subset A of  Z^d such that every element of  Z^d can be uniquely written in the form f+a, where f \in F and a\in A.The Periodic Tiling Conjecture states that if F is given and there is a tiling A of  Z^d by F, then there is also a periodic tiling  B of  Z^d by F. This statement is easy for d=1, and it was proved recently for d=2 by  Bhattacharya. The conjecture is still open for d>2.

In this talk we sketch a proof for the d=2 case given by Greenfeld and Tao.

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).