This award will support a three week workshop on Mathematical Ideas Arising from Conformal Field Theory to be held July 17 - August 6, 1989 at the Aspen Center for Physics in Aspen, Colorado. The workshop will be under the direction of Professor Daniel Freed of the University of Chicago. The purpose of this workshop is to encourage and extend collaboration and research among mathematicians working on projects directly related to conformal field theory. Such ideas occur in the study of infinite dimensional algebras, loop groups, invariants of 3 and 4 dimensional manifolds, invariants of knots and links, and elliptic cohomology. Invitations to the workshop will be issued on the basis of applications submitted to the Aspen Center.