Mathematical Modeling
Mathematical models are used in every branch of science and engineering to explore the relationships between different variables and parameters in order to be able to quantify a system's behavior. It is often said that there are two distinct kinds of research problems: problems we can solve, and problems that we care about solving. This seemingly cynical statement highlights an important aspect of mathematical modeling: most realistic models are too difficult to solve analytically. Fortunately, idealized models often capture the essential features of a system while remaining simple enough to provide useful and general qualitative information about the dynamics. In my research, I focus on developing minimal mathematical models of biological and social phenomena. Past projects have involved the origins of left-handedness and path optimization used by animals.