9401411 Yang This project consists of two related parts. The first is a joint project with Richard Hain (also at Duke), in which they intend to study a new type of function, the "braid polylogarithms," which they hope will become a bridge between the important and much studied classical polylogarithms and the Grassman polylogarithms. The second topic is part of an ongoing program to study the close relationship between hyperbolic 3-manifolds and the third algebraic K-groups. Recently, there has been a renaissance of research on polylogarithms because of their interesting applications to many mathematical disciplines, including algebraic K-theory, number theory, hyperbolic geometry and conformal field theory. Applications are also found in theoretical physics. This research hopes to provide further understanding of the relationship between the two important types of polylogarithm functions: the classical polylogarithms and the Grassman polylogarithms, and to contribute to the further understanding of their applications to other mathematical fields. ***
