# 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.

### 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 W. Pardon. “Chern classes of automorphic vector bundles.” *Inventiones Mathematicae*, vol. 147, no. 3, Dec. 2002, pp. 561–612. *Scopus*, doi:10.1007/s002220100184.
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Pardon, W., and M. Stern. “Pure hodge structure on the L2-cohomology of varieties with isolated singularities.” *Journal Fur Die Reine Und Angewandte Mathematik*, vol. 533, 2001, pp. 55–80.

Pardon, W. L., and M. A. Stern. “L2 -∂-cohomology of complex projective varieties.” *Journal of the American Mathematical Society*, vol. 4, no. 3, Jan. 1991, pp. 603–21. *Scopus*, doi:10.1090/S0894-0347-1991-1102582-6.
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Pardon, W. L. “Intersection homology Poincaré spaces and the characteristic variety theorem.” *Commentarii Mathematici Helvetici*, vol. 65, no. 1, Dec. 1990, pp. 198–233. *Scopus*, doi:10.1007/BF02566603.
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Goresky, M., and W. Pardon. “Wu numbers of singular spaces.” *Topology*, vol. 28, no. 3, Jan. 1989, pp. 325–67. *Scopus*, doi:10.1016/0040-9383(89)90012-8.
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Pardon, W. L. “The L2-∂-cohomology of an algebraic surface.” *Topology*, vol. 28, no. 2, Jan. 1989, pp. 171–95. *Scopus*, doi:10.1016/0040-9383(89)90019-0.
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Pardon, W. L. “The L2-∂-cohomology of an algebraic surface.” *Topology*, vol. 28, no. 2, 1989, pp. 171–95.

Hsiang, W. C., and W. Pardon. “When are topologically equivalent orthogonal transformations linearly equivalent?.” *Inventiones Mathematicae*, vol. 68, no. 2, June 1982, pp. 275–316. *Scopus*, doi:10.1007/BF01394060.
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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*, vol. 102, no. 1, Jan. 1982, pp. 123–70. *Scopus*, doi:10.2140/pjm.1982.102.123.
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Hsiang, W. C., and W. Pardon. “Orthogonal transformations for which topological equivalence implies linear equivalence.” *Bulletin of the American Mathematical Society*, vol. 6, no. 3, Jan. 1982, pp. 456–61. *Scopus*, doi:10.1090/S0273-0979-1982-15016-9.
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