# 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.

Pardon, W. "Mod 2 semi-characteristics and the converse to a theorem of Milnor." *Mathematische Zeitschrift* 171.3 (1980): 247-268.
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Bass, H, and Pardon, W. "Some hybrid symplectic group phenomena." *Journal of Algebra* 53.2 (1978): 327-333.

Pardon, W. "An invariant determining the Witt class of a unitary transformation over a semisimple ring." *Journal of Algebra* 44.2 (1977): 396-410.

Pardon, W. "Local surgery and applications to the theory of quadratic forms." *Bulletin of the American Mathematical Society* 82.1 (January 1, 1976): 131-134.
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