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Jenny Harrison

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American mathematician For the character, see Jenny Harrison (Shortland Street).
Jenny Harrison
BornAtlanta, Georgia, US
EducationUniversity of Alabama (BA)
University of Warwick (PhD)
Known forContributions to geometric analysis, chainlets
Scientific career
FieldsMathematics
InstitutionsUniversity of California, Berkeley
Doctoral advisorChristopher Zeeman

Jenny Harrison is a professor of mathematics at the University of California, Berkeley.

Education and career

Harrison grew up in Tuscaloosa, Alabama. On graduating from the University of Alabama, she won a Marshall Scholarship which she used to fund her graduate studies at the University of Warwick. She completed her doctorate there in 1975, supervised by Christopher Zeeman. Hassler Whitney was her postdoctoral adviser at the Institute for Advanced Study, and she was also one of the Miller Research Fellows at Berkeley. She was on the tenured faculty at the University of Oxford (Somerville College) from 1978 to 1981, before returning to Berkeley as an assistant professor.

In 1986, after being denied tenure at Berkeley, Harrison filed a lawsuit based on gender discrimination. 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. 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.

Research contributions

Harrison specializes in geometric analysis and areas in the intersection of algebra, geometry, and geometric measure theory. She introduced and developed with collaborators a theory of generalized functions called differential chains 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 domains such as soap films, fractals, charged particles, and Whitney stratified spaces, placing them on the same footing as smooth submanifolds in the resulting calculus. The results include optimal generalizations and simplifications of the theorems of Stokes, Gauss and Green. She has pioneered applications of differential chains to the calculus of variations, physics, and continuum mechanics. Her solution to Plateau's problem is the first proof of existence of a solution to a universal Plateau's problem for finitely many boundary curves, taking into account all soap films arising in nature, including nonorientable films with triple junctions, as well as solutions of Jesse Douglas, Herbert Federer and Wendell Fleming.

As a graduate student at the University of Warwick, where Zeeman introduced her to Plateau's problem. She found a counterexample to the Seifert conjecture at Oxford. In a Berkeley seminar in 1983 she proposed the existence of a general theory linking these together, and the theory of differential chains began to evolve. Jenny Harrison and Harrison Pugh proved that the topological vector space of differential chains satisfies a universal property determined by two natural axioms. They used the theory to provide the first universal solution to Plateau's problem, including soap film regularity, building upon Harrison's earlier paper.

Awards and fellowships

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References

  1. ^ Selvin, Paul (1993). "Jenny Harrison Finally Gets Tenure in Math at Berkeley". Science. 261 (5119): 286. Bibcode:1993Sci...261..286S. doi:10.1126/science.261.5119.286. PMID 17836828.
  2. Jenny Harrison at the Mathematics Genealogy Project
  3. ^ Selvin, Paul (1991). "Does the Harrison Case Reveal Sexism in Math?". Science. 252 (5014): 1781–1783. Bibcode:1991Sci...252.1781S. doi:10.1126/science.252.5014.1781. PMID 17753244.
  4. Archived 2014-04-07 at the Wayback Machine Jenny Harrison, Operator calculus of differential chains and differential forms, to appear in the Journal of Geometric Analysis, arxiv posting January 2011, 89 pages
  5. ^ J. Harrison and H. Pugh, Topological Aspects of Differential Chains, Journal of Geometric Analysis, 22 (2012), no. 3, 685–690
  6. Harrison, J. (2014). "Soap Film Solutions to Plateau's Problem". Journal of Geometric Analysis. 24: 271–297. doi:10.1007/s12220-012-9337-x.
  7. Jesse Douglas, Solutions of the problem of Plateau, Transactions of the American Mathematical Society 33 (1931), 263–321
  8. Herbert Federer and Wendell Fleming, Normal and integral currents, The Annals of Mathematics 72 (1960), no. 3, 458–520
  9. Jenny Harrison, C 2 {\displaystyle C^{2}} counterexamples to the Seifert conjecture. Topology (journal)|Topology, vol. 27, no. 3, pp. 249–278, 1988
  10. Jenny Harrison, Journal of Geometric Analysis, January 2013, 24(1):271-297

External links

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