Jenny Harrison

Jenny Harrison (* 1949 in Atlanta , Georgia ) is an American mathematician who studies geometric analysis and geometric measure theory. She is a professor at the University of California, Berkeley .

Jenny Harrison

Life

Jenny Harrison grew up in Tuscaloosa and received her bachelor's degree from the University of Alabama in 1971 and her PhD in 1975 as a Marshall Scholar at the University of Warwick with Colin Rourke and Erik Christopher Zeeman (Counterexamples to the Denjoy Conjecture). As a post-doctoral student , she was at the Institute for Advanced Study with Hassler Whitney in 1975/76 . In 1976 she became an instructor at Princeton University and an assistant professor in 1978 and a professor at Berkeley in 1993, where she was a Miller Professor in 2007 and a Miller Fellow from 1977 to 1979.

She was visiting scholar at IHES (1978, 1982), lecturer at Oxford University from 1979 to 1982 and fellow at Somerville College, 1990/91 at MSRI , was at Isaac Newton Institute , 1989/90 visiting professor at Yale University , 1981 at IMPA , 1996/97 visiting professor at Rockefeller University and 1980 at the University of Maryland .

Her trial against the University of Berkeley attracted attention, which in 1986 refused her a permanent position ( tenure ), against which she sued for gender-related disadvantage. The case split the faculty at the time - mathematicians like Stephen Smale and Robion Kirby were against it, others like Morris Hirsch and James Yorke were in favor. An out-of-court settlement was reached in 1993 after a committee of seven scientists recommended the permanent position, and she was given a professorship at Berkeley.

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In her dissertation, she solved an assumption made by Arnaud Denjoy . Denjoy had suspected that every - diffeomorphism for sufficiently large r is topologically conjugated to a - diffeormorphism, to which Harrison gave a counterexample. In 1988 she gave a counter example to the Seifert conjecture , after Paul A. Schweitzer had given a counter example in 1974 . The conjecture says that every vector field on the 3-sphere has either a zero or a closed solution curve (with the vectors as tangents). ${\displaystyle C^{r}}$ ${\displaystyle C^{r+1}}$ ${\displaystyle C^{2}}$ ${\displaystyle C^{1}}$

In 1993 she generalized Stokes' theorem for non-smooth areas, whereby there is a correlation between the differentiability properties of the differential forms and those of the areas on which they are defined (the smoother the differential forms, the "rougher" the areas can be).

In the 2000s she developed a theory of generalized functions (differential chains) that are different from distributions or de Rham currents and, in Harrison's view, provide a new, strict basis for the idea of ​​the infinitesimals and thus a connection from the discrete to the continuum deliver. With this she was able to prove the existence and regularity of the soap bubble solution (after Frederick Almgren ) of the plateau problem (2012), whereby earlier solutions such as the original solution by Jesse Douglas and that of the geometric measurement theory by Herbert Federer and Wendell Fleming also through their theory are included. Other applications of their calculus are Whitney stratified spaces and fractals.

She is co-editor of the Journal of Geometric Analysis.

Fonts

• with Harrison Pugh: Topological aspects of differential chains, J. Geom. Analysis, 22, 2012, 685-690, Arxiv
• Operator calculus of differential chains and differential forms, J. Geom Analysis 2013, Arxiv
• with Harrison Pugh: Existence and Soap film regularity of solutions to Plateau's problem, J. Geom. Analysis, 2012, Arxiv
• Soap film solutions to Plateau's problem, J. Geom. Analysis 2013, Arxiv
• Denjoy Fractals, Topology, 28, 1989, 69-80
• Stokes Theorem for non smooth chains, Bulletin AMS, October 1993, Arxiv
• with Harrison Pugh: Plateau's problem, in: John Forbes Nash jr., Michael Th. Rassias (eds.), Open problems in mathematics, Springer 2016, pp. 273-302

Web links

• Homepage ( Memento from February 5, 2012 in the Internet Archive )

Individual evidence

1. ↑ Jenny Harrison in the Mathematics Genealogy Project (English)
2. ↑ Harrison, Unsmoothable Diffeomorphisms , Annals of Mathematics, Volume 102, 1975, pp. 85-94
3. ↑ counterexamples to the Seifert conjecture , Topology, 27, 1988, 249-278 ${\displaystyle C^{2}}$
4. ^ What she proved with Harrison Pugh, Topological aspects of differential chains