The mathematical notion of a group encapsulates our common idea of symmetry. Groups play an important role in mathematics, and their structure has profound impact in the solution of a variety of problems in pure and applied mathematics. Groups are often studied from different perspectives, putting an emphasis on qualitatively different features of their structure, and therefore leading to the resolution of problems that tend to be different in nature. The aim of this workshop is to bring together some of the leading figures in two of these areas, so that each can learn new problems and techniques from the other. This will help open new avenues of research which will advance the current state of the art.