One of the areas in which I have had some recent interest is one of metamaterials with their application to cloaking. The fundamental problem is to be able to design a cloak which would render a region invisible to either light or sound. The mathematical background was provided in two papers which were published in the same issue of Science about a decade ago. One by Leonhardt and the other by Pendry et. al. These papers were for electromagnetism but it is a rule of thumb that anything that works for light can be made to work for sound (except travel in vacuum if one were to be pedantic about these things). These initial ideas were quickly transferred to sound and subsequently to elastic waves (Norris, Cummer, Willis, and Milton are some important names in here). Since then the field has exploded. The goal is to make waves do something like this (simulations done in Comsol by Valentin Serey, graduate student at IIT):
