The Mathematical Sciences Postdoctoral Research Fellowships are awards to recent recipients of doctoral degrees. The fellowship is designed to provide 24 months of support divided into 18 academic months and 3 periods of two summer months. The recipient has the option of a Research Instructorship which allows the 18 months of academic support to be taken as 9 months of full-time support and 18 months of half-time support. Mathematical Sciences Postdoctoral Research Fellowship awards allow fellows to choose research environments that will have maximal impact on their future scientific development. Joe Kilian received his doctoral degree from the Massachusetts Institute of Technology, and will pursue research in the area of applied mathematics, specifically, theoretical computer science, focussing on the subfield of abstract cryptography, under the guidance of Michael Rabin at Harvard University and Shafi Goldwasser at the Massachusetts Institute of Technology.