9508777 Brannen This award provides support for a 12-month Japan Society for the Promotion of Science Postdoctoral Fellowship for Dr. Noah Brannen of the University of California at Davis. The fellowship will allow Dr. Brannen to collaborate with Dr. Tadashi Nagano of Sophia University. Together they hope to prove Petty's conjecture, a statement involving the relationship between the volume of a convex body and that of its projection body. The conjecture is considered by many to be the outstanding unsolved problem in the field of affine isoperimetric inequalities. Dr. Nagano was the recipient of last year's Outstanding Research Award in Geometry from the Mathematical Association of Japan. There are areas in Dr. Brannen's approach to proving the conjecture in which Dr. Nagano is uniquely qualified to provide invaluable assistance. Their collaboration will quite possibly allow them to solve this difficult problem, and will definitely provide an opportunity for the exchange of mathematical ideas and techniques. Dr. Brannen hopes that his experience in Japan will lead to fruitful collaborative efforts with Dr. Nagano and other mathematicians in Japan. ***
