The International Research Fellow Awards Program enables U.S. scientists and engineers to conduct three to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will provide twelve months of support to Dr. David L. Savitt to work with Dr. Christophe Breuil at the Universite Paris-Sud in Orsay, France on the modularity of some geometric Galois recommendations. This project is co-funded by the Math and Physical Science Directorate's Office of Multidisciplinary Activities. This research is part of a program to investigate the following fundamental question of arithmetic algebraic geometry: when can a representation of the absolute Galois group of the rational numbers be found in geometry? For example, results in this direction were the crux of Wiles's proof of Fermat's Last Theorem. The arithmetic geometry group at Paris-Sud is one of the largest and most active in the world. In addition to Breuil, the faculty at Orsay includes, among others, Laurent Clozel, Jean-Louis Colliot-Thelene, Jean-Marc Fontaine, Guy Henniart, Luc Illusie, Laurent Lafforgue, Gerard Laumon, Bernadette Perrin-Riou, Michel Raynaud, and Lucien Szpiro. ***
