## Research Interests for William L. Pardon

**Research Interests:** *Algebra and Geometry of Varieties*
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**
- Goresky, M; Pardon, W,
*Chern classes of automorphic vector bundles*,
Inventiones Mathematicae, vol. 147 no. 3
(2002),
pp. 561-612 [doi]
- Pardon, W; Stern, M,
*Pure hodge structure on the L*_{2}-cohomology of varieties with isolated singularities,
Journal fur die Reine und Angewandte Mathematik, vol. 533
(2001),
pp. 55-80
- Pardon, WL; Stern, MA,
*L*^{2} -âˆ‚-cohomology of complex projective varieties,
The Journal of the American Mathematical Society, vol. 4 no. 3
(January, 1991),
pp. 603-621 [doi]
- Pardon, WL,
*Intersection homology PoincarĂ© spaces and the characteristic variety theorem*,
Commentarii Mathematici Helvetici, vol. 65 no. 1
(1990),
pp. 198-233, ISSN 0010-2571 [doi]
- Goresky, M; Pardon, W,
*Wu numbers of singular spaces*,
Topology, vol. 28 no. 3
(1989),
pp. 325-367, ISSN 0040-9383 [doi]