In  an old question of de Rham about the topological classification of rotations of Euclidean space was largely answered in the affirmative.
Methods of algebraic K-theory were used to study quadratic forms defined over an affine k-algebra in  and , and to relate their properties to geometric properties of the variety underlying the k-algebra ().
More recently Professor Pardon has studied the algebraic topology and differential geometry of singular spaces (, , ). In particular  and  examine how the singularities of a space limit the existence of characteristic classes; on the other hand, in the case of arbitrary Hermitian locally symmetric spaces,  shows how characteristic classes on the smooth locus may be extended canonically over the singularities, even when the tangent bundle does not so extend.
Paper  looks at the arithmetic genus, in the sense of L2-cohomology, of singular algebraic surfaces. In  Professor Pardon and Professor Stern verify a conjecture of MacPherson and settle the questions partially answered in ; in  they give an analytic description of the Hodge structure on the intersection homology of a variety with isolated singularities.