This award supports a conference entitled: "Lie Groups, Lie Algebras and their Representations". The conference will be a series of five seminar weekends, over the course of the academic year, held at various campuses of the University of California. The two objectives of the conference project are: 1. Fostering interactions between institutions separated by significant physical distances; 2. Permitting exchange of ideas between UC faculty and students, on the one hand, and several distinguished experts in Representation Theory, newly arrived from the former Soviet Union. This format permits the entire California mathematical community and its graduate students to take advantage of the presence of these experts.