William L. Pardon

William L. Pardon
  • Professor of Mathematics
External address: 219 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2838
Office Hours: 

T, 1:30-3:00
W, 12:00-2:30

Research Areas and Keywords

Algebra & Combinatorics
Commutative algebra, Quadratic forms
Analysis
Singular spaces
Geometry: Differential & Algebraic
Singular spaces, Quadratic forms
Number Theory
Commutative algebra, Quadratic forms
Topology
Singular spaces

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.

Education & Training
  • Ph.D., Princeton University 1974

  • B.A., University of Michigan at Ann Arbor 1969

Selected Grants

Quadratic Forms on Schemes awarded by National Science Foundation (Principal Investigator). 2000 to 2005

(95-0296) Geometry & Topology of Singular Spaces awarded by National Science Foundation (Principal Investigator). 1995 to 1998

(96-0506) Geometry & Topology of Singular Spaces awarded by National Science Foundation (Principal Investigator). 1995 to 1998

(97-0879) Geometry and Topology of Singular Spaces awarded by National Science Foundation (Principal Investigator). 1995 to 1998

(94-0810) Mathematical Sciences: Topology and Geometry of Algebraic Varieties awarded by National Science Foundation (Principal Investigator). 1992 to 1996

(92-0265) Mathematical Sciences: Topology and Geometry of Algebraic Varieties awarded by National Science Foundation (Principal Investigator). 1992 to 1995

(94-0057) Mathematical Sciences: Topology and Geometry of Algebraic Varieties awarded by National Science Foundation (Principal Investigator). 1992 to 1995

(90-0234) Geometry of Singular Spaces awarded by National Science Foundation (Principal Investigator). 1990 to 1992

(88-0222) Geometry of Singular Spaces awarded by National Science Foundation (Principal Investigator). 1987 to 1990

(86-0080) Topology of Singular Spaces awarded by National Science Foundation (Principal Investigator). 1986 to 1988

Goresky, M, and Pardon, W. "Chern classes of automorphic vector bundles." Inventiones Mathematicae 147.3 (March 1, 2002): 561-612. Full Text

"Pure hodge structure on the L2-cohomology of varieties with isolated singularities." Journal Fur Die Reine Und Angewandte Mathematik 533 (December 1, 2001): 55-80.

Pardon, WL, and Stern, MA. "$L\sp 2\text–\overline\partial$-cohomology of complex projective varieties." Journal of the American Mathematical Society 4.3 (September 1, 1991): 603-603. Full Text

Pardon, WL. "Intersection homology Poincaré spaces and the characteristic variety theorem." Commentarii Mathematici Helvetici 65.1 (December 1990): 198-233. Full Text

Pardon, WL. "The L2−∂¯-cohomology of an algebraic surface." Topology 28.2 (1989): 171-195. Full Text

Pardon, WL. "The L2-∂-cohomology of an algebraic surface." Topology 28.2 (1989): 171-195.

Goresky, M, and Pardon, W. "Wu numbers of singular spaces." Topology 28.3 (1989): 325-367. Full Text

Hsiang, W-C, and Pardon, W. "When are topologically equivalent orthogonal transformations linearly equivalent?." Inventiones Mathematicae 68.2 (June 1982): 275-316. Full Text

Hsiang, W-C, and Pardon, W. "Orthogonal transformations for which topological equivalence implies linear equivalence." Bulletin of the American Mathematical Society 6.3 (May 1, 1982): 459-462. Full Text

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