Analysis & Applied Math

Computing eigenpairs of constant elliptic operators for all but the simplest domains is a challenging task. We'd like to compute eigenpairs to high accuracy, and we'd like to do this efficiently. In this talk, we'll survey a rather natural approach via boundary integral operators, which reduces the (volumetric) eigenproblem to a problem on the boundary. We'll show how this approach can be used for domains with smooth boundary as well as polygonal domains. We'll then describe some questions in spectral geometry which can be explored with this method. While the talk focuses on problems in the plane, the approach generalizes readily to $\mathbb{R}^3$.

Nilima also has some super-cool research "Skeletal muscles: modeling and simulation" that she'd be happy to discuss with anyone who asks. :)