Overview
In [1] 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 [2] and [4], and to relate their properties to geometric properties of the variety underlying the k-algebra ([3]).
More recently Professor Pardon has studied the algebraic topology and differential geometry of singular spaces ([5], [6], [10]). In particular [5] and [6] 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, [10] 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 [7] looks at the arithmetic genus, in the sense of L2-cohomology, of singular algebraic surfaces. In [8] Professor Pardon and Professor Stern verify a conjecture of MacPherson and settle the questions partially answered in [7]; in [9] they give an analytic description of the Hodge structure on the intersection homology of a variety with isolated singularities.
Current Appointments & Affiliations
Recent Publications
Chern classes of automorphic vector bundles
Journal Article Inventiones Mathematicae · December 1, 2002 Full text CitePure hodge structure on the L2-cohomology of varieties with isolated singularities
Journal Article Journal fur die Reine und Angewandte Mathematik · 2001 CiteL2 -∂-cohomology of complex projective varieties
Journal Article Journal of the American Mathematical Society · January 1, 1991 Full text CiteRecent Grants
Quadratic Forms on Schemes and Geometry of Varieties
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2000 - 2005Geometry and Topology of Singular Spaces
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1995 - 1998Geometry & Topology of Singular Spaces
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1995 - 1998View All Grants