Many interesting physical phenomena are difficult to pin down mathematically, which is a necessary first step in order to make predictions confidently. This is particularly true in the study of the evolution of defects in materials; for example, predicting the growth and paths of cracks. My research is in applied analysis, and my goals are to formulate mathematically- and physically-reasonable models for these problems, as well as understand the properties of solutions (even proving their existence itself is often a serious problem). At WPI, I involve both graduate and undergraduate students in these projects, who often make important contributions.