The goal of our research program Doped Semiconductor Alloy Nanostructures is to develop and explore a mathematical theory to describe our new process for creating semiconductor nanostructures consisting of an alloy of two compound semiconductors separated into two regions with a continuously changing gradation between them. This arrangement creates a smooth variation in the conduction and valence bands across the nanostructure. By varying the parameters that control this process, we can create various profiles that will give rise to enhanced electronic and optical properties, such as increased light emission and absorption, reduced nonradiative Auger rates, and ultrafast carrier separation. We will utilize recent advances in nanoscale cation exchange to achieve these goals and employ a novel approach called "arrested cation exchange". We seek a bright, motivated, mathematically trained postdoctoral researcher who is experienced working with systems of coupled diffusion equations to explore their implications for our goal of creating alloyed nanocrystals.