| DATE: | Thursday, April 19, 2001 |
| TIME: | 4:30-5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Natasha Jonoska |
| TITLE: | The Symbolic Dynamics of Multidimensional Tiling Systems |
We consider tilings of d-dimensional lattice of the integers. A set of prototiles P is a finite set of finite subsets of Z^d. A tiling of Z^d is a disjoint union of translates of the prototiles which equals Z^d. The set of all such tilings for a given set of prototiles is a tiling system. We investigate the relationship between tiling systems and certain symbolic dynamics systems. For every dimension d, every shift of finite type is conjugate to a power of a tiling system, but there are tiling systems that are not conjugate to any shift of finite type. However, the set of topological entropies of shifts of finite type coincides with the set of topological entropies of the tiling systems.