### Lecturer

#### Steve Jackson, University of North Texas

The combinatorics of abelian group actions on Polish spaces has been the subject of recent investigation, and is (somewhat surprisingly) interesting and non-trivial. If one considers the actions of $Z^n$, we see a pattern develop: problems which are easy for $n=1$ become much more difficult for n at least 2. We discuss three example of this phenomenon: the subshift, graph homomorphism and tiling problems. For the first two problems, we show the questions are undecidable for n at least 2 , while for the third problem the question is open.

#### Part of the Semester : Descriptive set theory and Polish groups

Name University Dates of visit
Steve Jackson University of North Texas 08/02/2018 - 08/02/2018
Total Guests : 1
Name University Dates of visit
Total Guests : 0