This talk gives an elementary introduction to some recent work on
arithmetic progression and summarizes some of the topics discussed at
the recent Oberwolfach Arbeitsgemeinschaft "Ergodic Theory and
Combinatorial Number Theory".
The talk includes a more detailed discussion of a result of Hillel
Furstenberg and Benji Weiss which produces monochromatic binary subtrees
of colored trees, generalizing van der Waerden's theorem and Szemeredi's
theorem.