This award will support the participation of U.S. researchers in a seminar on the "Mapping of Operator Algebras," organized jointly by Professor Richard Kadison of the University of Pennsylvania and Professor Huzihiro Araki of Kyoto University, Japan. United States, Japanese and invited third-country participants will meet at the University of Pennsylvania during May 1988. The seminar will be devoted to discussions of recent developments in the subject of mappings of operator algebras and to the applications that have been and are being made of these developments to our understanding of non-commutative analysis and geometry. The field of operator algebras is rapidly advancing, with scientists from both the United States and Japan at the forefront of this research. This seminar will provide a forum for the exchange of ideas, particularly in the application of operator algebras to other fields of science such as physics.