Creative Research Medal 2013
Daniel Krashen, associate professor of mathematics, is recognized for his contributions to a branch of algebra known as “field patching.” Field patching assigns geometric shapes to complex algebraic systems called function fields. The method uses the tools of topology—an area of mathematics concerned with describing shapes—to more easily scrutinize the properties of equations in function fields. These are pure mathematical problems requiring great technical knowledge to understand and solve. While it is difficult to predict how or when discoveries in this field might translate into applied technologies for biology, physics or engineering, Krashen’s research creates an essential scaffolding from which applied technologies may emerge. These algebraic structures have deep underpinnings in the understanding of fundamental applications of mathematics from the symmetries and structure of space, time and matter, to the optimization of error-correcting codes in cell-phone communication.