# 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

##### Analysis

##### Geometry: Differential & Algebraic

##### Number Theory

##### Topology

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.

### 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.
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"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.
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Pardon, WL. "Intersection homology Poincaré spaces and the characteristic variety theorem." *Commentarii Mathematici Helvetici* 65.1 (December 1990): 198-233.
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Pardon, WL. "The L2−∂¯-cohomology of an algebraic surface." *Topology* 28.2 (1989): 171-195.
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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.
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Pardon, W. "The exact sequence of a localization for Witt groups. II. Numerical invariants of odd-dimensional surgery obstructions." *Pacific Journal of Mathematics* 102.1 (September 1, 1982): 123-170.
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Hsiang, W-C, and Pardon, W. "When are topologically equivalent orthogonal transformations linearly equivalent?." *Inventiones Mathematicae* 68.2 (June 1982): 275-316.
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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.
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