My research is divided into two main categories: i) theoretical studies of self-assembly, and ii) mathematical biology.
With regards to self-assembly, the overarching question is can we harness the natural assembly process so that `human-made objects' are made spontaneously? – thereby expanding the realm of what we can make, and the ease with which we can make it. Spherical colloidal particles are a natural model system for studying self-assembly because i) conditions that cause them to bind to one another, and thus to self-assemble into packings, are well-known, and ii) the diversity of structures that can be constructed out of sphere packings is virtually limitless. My research thus far has focused on studying self-assembly via the packing of spheres, and interesting physical and mathematical questions have arisen from this.
I am also interested in biological systems. My research thus far has focused on theoretical and experimental studies of aging, and on developing mathematical methods to extract essential features of biological signaling networks. With respect to the latter, because biological systems contain many components, it is common for them to be modeled using large systems of differential equations. However, current mathematical techniques are incapable of determining how solutions to large systems of equations depend on their parameters. We have shown that large systems of equations can be reduced to smaller systems, which are sometimes analytically tractable. These small systems are of biological interest, because they can be used to make predictions about the underlying biology, and are falsifiable. Additionally, interesting mathematical questions arise when considering generalizations of this reduction method.