The about blurb:
Geometric group theory lies at the crossroads of geometry, topology, and group theory, yet many of its questions can be attacked by undergraduates. In the first two weeks of the REU, we will explore what it means for a group to have a geometry. We'll start with a hands-on introduction to non-Euclidean geometries, tilings, how to draw graph pictures of groups, and how groups can act on spaces. We will also look at an assortment of groups arising from topology and geometry, such as braid groups, reflection groups, and fundamental groups of surfaces. We will discuss algorithmic questions, such as how to tell when two strings of group generators actually determine the same element in the group.
And the "Statement of Interest" is your standard 1-2 page why do you want to do this REU, what are your interests, mathematical or otherwise, your career plans (pure mathematician or mathematical/theoretical physicist? who knows?!) and other info.
What do people look for? I highly doubt that they care about my interest in circus, so I'm safe there. ;)