Research Interests for William L Pardon

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.

Recent Publications

1. Mark Goresky, William L. Pardon, Chern classes of modular varieties, Inventiones Math., v. 147 (2002), 561-612  [abs]
2. William Pardon, Mark Stern, Pure Hodge Structure on the L2-cohomology of Varieties with Isolated Singularities, Journal fur die Reine und Angewandte Mathematik, v. 533 (2001), 55-80 [available here]
3. William Pardon, The filtered Gersten-Witt resolution for regular schemes (Preprint, 0) [http://www.math.uiuc.edu/K-theory/0419/index.html], [available here]
4. William L. Pardon, Mark Stern, L2 -- a cohomology of Complex Projective Varieties, Journal of AMS, 4, 1991, pp. 603-621
5. William L. Pardon, Intersection Homology Poincare Spaces and the Characteristic Variety Theorem, Comm. Math. Helv., 65, 1990, pp. 198-223