Mathematics Graduate Students Organization

Seminar:

Date: March 26

We give an introduction to the theory of symbolic dynamics on groups and tiling problems. We will define two types of periodicity for configurations (tilings) on arbitrary groups and discuss the following question: given a group G, does every shift of finite type on G contain a periodic configuration? Historically, the answer has been known to be "yes" for $\scriptstyle{\mathbb{Z}}$ and "no" for $\scriptstyle{\mathbb{Z}^2}$. We present some new results giving partial answers to this question. This is a joint work with Andrew Penland.