William L. Pardon, Professor
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 Ktheory were used to study quadratic forms defined over an affine kalgebra in [2] and [4],
and to relate their properties to geometric properties of the variety underlying the kalgebra ([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 L2cohomology, 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.
 Contact Info:
Teaching (Spring 2018):
 MATH 431.01, ADVANCED CALCULUS I
Synopsis
 Physics 119, WF 08:30 AM09:45 AM
 Office Hours:
 T, 1:303:00
W, 12:002:30
 Education:
Ph.D.  Princeton University  1974 
B.A.  University of Michigan at Ann Arbor  1969 
 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 Ktheory were used to study quadratic forms defined over an affine kalgebra in [2] and [4],
and to relate their properties to geometric properties of the variety underlying the kalgebra ([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 L2cohomology, 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 Ph.D. Students
(Former Students)
 Recent Publications
(More Publications)
 Goresky, M; Pardon, W, Chern classes of automorphic vector bundles,
Inventiones Mathematicae, vol. 147 no. 3
(2002),
pp. 561612 [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. 5580
 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. 603621 [doi]
 Pardon, WL, Intersection homology PoincarĂ© spaces and the characteristic variety theorem,
Commentarii Mathematici Helvetici, vol. 65 no. 1
(1990),
pp. 198233, ISSN 00102571 [doi]
 Goresky, M; Pardon, W, Wu numbers of singular spaces,
Topology, vol. 28 no. 3
(1989),
pp. 325367, ISSN 00409383 [doi]
