Edgar H. Brown will extend real and rational homotopy theory and apply it to classifying spaces coming from Lie algebras and foliations. Jerome Levine will study problems in link concordance, algebraic closure of groups and proposed new link invariants. Kiyoshi Igusa plans to continue his investigation into the relationship between algebraic K-theory and smooth manifolds. He also intends to apply algebraic K-theory and cyclic homology to the representation theory of finite dimensional algebras. Daniel Ruberman will continue his work on gauge theory and geometric invariants of 3-manifolds. Applications in knot theory, and the study of surfaces in 4-manifolds will be pursued.
