A six-week research cluster on the Mathematics of Polygonal Billiards will be held at Tufts University from July 3-August 11, 2017. The group will consist of three faculty, three graduate students, and three undergraduates—not already experts in mathematical billiards—coming together to engage in a mix of research projects and experimental work. The program will have a rotating roster of visiting experts in the first five weeks to teach the recent developments and propose new directions for investigation. In the sixth week, the focus will turn to writing, which will continue past the end of the program. The cluster is expected to produce research articles and computer tools.