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## 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
1. Goresky, M; Pardon, W, Chern classes of automorphic vector bundles, Inventiones Mathematicae, vol. 147 no. 3 (March, 2002), pp. 561-612, Springer Nature [doi]
2. Pardon, W; Stern, M, Pure hodge structure on the L2-cohomology of varieties with isolated singularities, Journal Fur Die Reine Und Angewandte Mathematik, vol. 533 (December, 2001), pp. 55-80
3. Pardon, WL; Stern, MA, $L\sp 2\text–\overline\partial$-cohomology of complex projective varieties, Journal of the American Mathematical Society, vol. 4 no. 3 (September, 1991), pp. 603-603, American Mathematical Society (AMS) [doi]
4. Pardon, WL, Intersection homology Poincaré spaces and the characteristic variety theorem, Commentarii Mathematici Helvetici, vol. 65 no. 1 (December, 1990), pp. 198-233, European Mathematical Publishing House, ISSN 0010-2571 [doi]
5. Goresky, M; Pardon, W, Wu numbers of singular spaces, Topology, vol. 28 no. 3 (1989), pp. 325-367, Elsevier BV, ISSN 0040-9383 [doi]

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