Research Interests for William L. Pardon
Research Interests: Algebra and Geometry of Varieties
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.
- Recent Publications
- Goresky, M; Pardon, W, Chern classes of automorphic vector bundles,
Inventiones Mathematicae, vol. 147 no. 3
pp. 561-612, Springer Nature [doi]
- 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
- Pardon, WL; Stern, MA, L2 -∂-cohomology of complex projective varieties,
Journal of the American Mathematical Society, vol. 4 no. 3
pp. 603-621, American Mathematical Society (AMS) [doi]
- Pardon, WL, Intersection homology Poincaré spaces and the characteristic variety theorem,
Commentarii Mathematici Helvetici, vol. 65 no. 1
pp. 198-233, European Mathematical Publishing House, ISSN 0010-2571 [doi]
- Goresky, M; Pardon, W, Wu numbers of singular spaces,
Topology, vol. 28 no. 3
pp. 325-367, Elsevier BV, ISSN 0040-9383 [doi]