Jenny Harrison

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 operator 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 differential chains which place soap films, fractals, and charged particles, on the same footing as smooth submanifolds. 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 operator calculus (called chainlet geometry in) to the calculus of variations, physics, and numerical analysis.

Harrison grew up in Tuscaloosa, Alabama. Her graduate studies were at the University of Warwick, where E.C. Zeeman introduced her to Plateau's Problem. Hassler Whitney was her postdoctoral adviser at the Institute for Advanced Study. After her time at the Institute, she became an instructor at Princeton University. She found a counterexample to the Seifert conjecture while on the faculty at Oxford University. She was struck by the duality between differentiability class of functions, and Hausdorff dimension of domains manifested in her work, as well as Sard's Theorem and Denjoy's Theorem, and observed, "The smoother the function, the rougher can be the domains in many contexts." In a Berkeley seminar in 1983 she proposed the existence of a general theory linking these together, and Operator Calculus began to evolve.

Jenny Harrison and Harrison Pugh recently proved that Operator Calculus is distinct from the theory of Schwartz distributions and de Rham currents, settling a question posed by Michael Atiyah in 1996. Furthermore, their paper showed the topological vector space of differential chains is uniquely determined by four simple axioms.

Harrison initiated a lawsuit based on gender 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. Stephen Smale and Robion Kirby were the most vocal opponents to her receiving tenure during the case, while Morris Hirsch and James Yorke were her most vocal supporters.