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.

Office Location: | 219 Physics Bldg, Durham, NC 27708 |

Office Phone: | (919) 660-2838 |

Email Address: | |

Web Page: | http://www.math.duke.edu/~wlp |

**Teaching (Spring 2018):**

- MATH 431.01,
*ADVANCED CALCULUS I*Synopsis- Physics 119, WF 08:30 AM-09:45 AM

**Office Hours:**- T, 1:30-3:00

W, 12:00-2:30

**Education:**Ph.D. Princeton University 1974 B.A. University of Michigan at Ann Arbor 1969

**Research Interests:***Algebra and Geometry of Varieties*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.

**Current Ph.D. Students**

**Recent Publications**- Goresky, M; Pardon, W,
*Chern classes of automorphic vector bundles*, Inventiones Mathematicae, vol. 147 no. 3 (2002), pp. 561-612 [doi] - Pardon, W; Stern, M,
*Pure hodge structure on the L*, Journal fur die Reine und Angewandte Mathematik, vol. 533 (2001), pp. 55-80_{2}-cohomology of varieties with isolated singularities - Pardon, WL; Stern, MA,
*L*, The Journal of the American Mathematical Society, vol. 4 no. 3 (January, 1991), pp. 603-621 [doi]^{2}-âˆ‚-cohomology of complex projective varieties - Pardon, WL,
*Intersection homology PoincarĂ© spaces and the characteristic variety theorem*, Commentarii Mathematici Helvetici, vol. 65 no. 1 (1990), pp. 198-233, ISSN 0010-2571 [doi] - Goresky, M; Pardon, W,
*Wu numbers of singular spaces*, Topology, vol. 28 no. 3 (1989), pp. 325-367, ISSN 0040-9383 [doi]

- Goresky, M; Pardon, W,