Jenny Harrison

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Jenny Harrison is a professor of mathematics at UC Berkeley. She specializes in geometric analysis and areas in the intersection of algebra, geometry, and geometric measure theory. Her most important contribution to mathematics has come in recent years when she developed a theory of quantum calculus that unifies an infinitesimal calculus with the classical theory of the smooth continuum, a long outstanding problem. The infinitesimals are constructive and arise from methods of standard analysis, as opposed to the nonstandard analysis of Abraham Robinson. The methods apply equally well to a large class of domains called chainlets which include soap films, fractals, graphs of L1 functions, charged particles, as well as smooth manifolds. The results include optimal generalizations and simplifications of the theorems of Stokes, Gauss and Green. She is also known for her counterexamples to the Denjoy conjecture and a version of the Seifert conjecture. She has pioneered applications of chainlet geometry to the calculus of variations, physics, and numerical analysis.

Harrison was born in Atlanta, Georgia. Her graduate studies were at the University of Warwick, and Hassler Whitney was her postdoctoral advisor at the Institute for Advanced Study. After her time at the Institute, she became an instructor at Princeton University, where she learned of the Seifert conjecture. She found a counterexample while on the faculty at Oxford University. Harrison's work on chainlets built upon her earlier work on the Denjoy and Seifert conjectures, where she was struck by the duality between differentiability class of functions and Hausdorff dimension of domains.

Harrison initiated a lawsuit based on sex discrimination in the 1986 tenure decision by the Berkeley mathematics department. The case attracted international attention. The 1993 settlement led to a new review of her work by a panel of seven mathematicians and science faculty who unanimously recommended tenure as a full professor. The review included her generalization of Stokes' theorem to nonsmooth domains. Robion Kirby was the most vocal opponent to her receiving tenure during the case.

[edit] Selected works

Unsmoothable diffeomorphisms. Annals of Mathematics, vol. 102, pp. 85-94, 1975.
Stokes' theorem for nonsmooth chains. Bulletin of the American Mathematical Society, October, 1993.
C2 counterexamples to the Seifert conjecture. Topology, vol. 27, no. 3, pp. 249-278, 1988.
On Plateau's problem for soap films with bounded energy, Journal of Geometric Analysis, Volume 14, Number 2, 2004.
Differential complexes and exterior algebra, arXiv posting January 9, 2006, 50 pages. math-ph/0601015
Lecture notes on chainlet geometry - new topological methods in geometric measure theory, arXiv posting May 24, 2005, 153 pages, Proceedings of the Ravello Summer School for Mathematical Physics, 2005