Creative Research Medal 2011
Joseph Fu, professor of mathematics, is a leading authority on integral geometry, the mathematical structure behind the transforms used in CAT scans, MRIs, and crystal diffraction that reconstruct three dimensional images from multi-perspective two dimensional data. His research seeks to develop relationships between integral quantities, such as the volume of a solid body and the areas of planar slices of the body.
Although certain elementary cases had been understood since the 1930s, the much more complicated case of so-called “hermitian integral geometry” resisted solution until 2006, when Fu discovered a mysterious underlying algebraic structure. The full implications were then explained in a series of papers by Fu and his collaborators between 2006 and 2009. These papers also describe possible useful machinery for handling the integral quantities and their transforms in this new case.