This grant is for continued investigation of the interaction between mixed Hodge theory, 1-adic cohomology, rational homotopy, etale homotopy and the topology of singularities of algebraic varieties. The theory of mixed Hodge structures, recently developed by Deligne, is a powerful tool with potentially far- reaching applications to singularities. Investigation will continue into the consequences of the existence of a mixed Hodge structure on the rational homotopy of links of the singular set of varieties. In particular, restrictions will be put on the knot type of links. The purity of their cohomology will be investigated, and an 1-adic minimal model will be found for them. It is important to master powerful techniques for handling singularities, since mathematical models of aspects of the real world are seldom smooth everywhere but exhibit essential singularities.
