# 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 and Geometry of Varieties awarded by National Science Foundation (Principal Investigator). 2000 to 2005

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

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

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

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

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

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

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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