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William L. Pardon, Professor

William L. Pardon

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.

Contact Info:
Office Location:  219 Physics Bldg, Durham, NC 27708
Office Phone:  (919) 660-2838
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~wlp

Teaching (Fall 2017):

  • MATH 212.07, MULTIVARIABLE CALCULUS Synopsis
    Physics 259, WF 10:05 AM-11:20 AM
  • MATH 431.01, ADVANCED CALCULUS I Synopsis
    Physics 119, WF 08:30 AM-09:45 AM
Teaching (Spring 2018):

  • MATH 431.01, ADVANCED CALCULUS I Synopsis
    Physics 259, WF 08:30 AM-09:45 AM
Office Hours:

T, 1:30-3:00
W, 12:00-2:30
Education:

Ph.D.Princeton University1974
B.A.University of Michigan at Ann Arbor1969
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   (Former Students)

    Recent Publications   (More Publications)

    1. Goresky, M; Pardon, W, Chern classes of automorphic vector bundles, Inventiones Mathematicae, vol. 147 no. 3 (2002), pp. 561-612 [doi]
    2. Pardon, W; Stern, M, 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
    3. Pardon, WL; Stern, MA, L2 -∂-cohomology of complex projective varieties, The Journal of the American Mathematical Society, vol. 4 no. 3 (January, 1991), pp. 603-621 [doi]
    4. Pardon, WL, Intersection homology Poincaré spaces and the characteristic variety theorem, Commentarii Mathematici Helvetici, vol. 65 no. 1 (1990), pp. 198-233, ISSN 0010-2571 [doi]
    5. Goresky, M; Pardon, W, Wu numbers of singular spaces, Topology, vol. 28 no. 3 (1989), pp. 325-367, ISSN 0040-9383 [doi]

     

    dept@math.duke.edu
    ph: 919.660.2800
    fax: 919.660.2821

    Mathematics Department
    Duke University, Box 90320
    Durham, NC 27708-0320