Presidential Lectures

Integral equation methods play an important role in the numerical simulation of electromagnetic scattering. They are easy to employ in complex geometry and impose the desired radiation conditions at infinity without the need for artificial numerical boundaries. Two of the obstacles faced by current forward simulation tools are “low-frequency breakdown” and the lack of easy to use high order quadrature rules for complicated surfaces. In this talk, I will review the relevant background material, discuss a new mathematical formalism for scattering from perfect conductors and briefly describe a new quadrature technique that yields easily implementable high order rules for singular and weakly singular integrals. The scheme, denoted QBX (quadrature by expansion) is compatible with fast hierarchical algorithms such as the fast multipole method.

New evidence of exoplanets reveals a higher-than-expected occurrence of potentially habitable worlds in our galactic neighborhood. What does this evidence tell us about life on other planets? How can we search for signs of life on other planets?

In biological systems, there are striking examples where complicated structures (i.e., the bacterial ribosome) can spontaneously assemble, driven by specific interactions between the components. But how can systems be designed to have this property? Recent technological  advances have created the opportunity for making technologically relevant systems that self assemble, using strands of DNA or objects coated with DNA. We will use these systems as inspiration to formulate theoretical models to understand how self assembly works in these systems, through theory, numerical simulation and experiment — and start to speculate as to whether resulting principles might be useful for unravelling the rules of biological self-assembly.

L. Mahadevan will explain how a combination of biological and physical experiments, together with mathematical models and computations, begin to unravel the physical basis for morphogenesis. He will go on to explore how these pan-disciplinary problems enrich the origins of this topic, creating new questions in mathematics, physics and biology.