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

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

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

(92-0265) 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 (2002): 561-612. Full Text

Pardon, W, and Stern, M. "Pure hodge structure on the L2-cohomology of varieties with isolated singularities." Journal fur die Reine und Angewandte Mathematik 533 (2001): 55-80.

Pardon, WL, and Stern, MA. "L2 -∂-cohomology of complex projective varieties." Journal of the American Mathematical Society 4.3 (January 1, 1991): 603-621. Full Text

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

Pardon, WL. "The L2-∂-cohomology of an algebraic surface." Topology 28.2 (January 1, 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. "Orthogonal transformations for which topological equivalence implies linear equivalence." Bulletin of the American Mathematical Society 6.3 (May 1, 1982): 459-462. Full Text

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

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