Gigliola Staffilani, the Abby Rockefeller Mauzé Professor of Mathematics at the Massachusetts Institute of Technology, is interested in the study of partial differential equations (PDE) of the dispersive type. These equations are used in physics to describe wave phenomena. Since the phenomena are complex, the proposed PDE that describe them are not in closed forms—explicit solutions cannot be written for them—so mathematicians must develop sophisticated abstract mathematical tools to recover their properties in an indirect way. Although Staffilani does not use numerical methods in her research, her results validate some numerical findings. Conversely, numerical predictions guide her in an abstract investigation using Fourier analysis, harmonic analysis, analytic number theory, and differential geometry.
At Radcliffe, Staffilani will extend the study of dispersive equations to include elements of probability. In nature, many phenomena occur not in a deterministic manner but in a probable sense; being able to understand if a phenomenon is “rare” is not just interesting, but useful. She will also undertake a more refined study of certain multidimensional dispersive equations that have different periods for different coordinates. The fascinating aspect of this problem is that it can be attacked from both an experimental point of view and a theoretical one involving number theory. She will collaborate with Andrea R. Nahmod.
After receiving a PhD from the University of Chicago, Staffilani became a faculty member at Stanford, Princeton, and Brown universities. She has twice been a member of the Institute for Advanced Study in Princeton. She received several National Science Foundation grants and a Sloan Research Fellowship.