Jenny Harrison is a professor of mathematics at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

Education and career

Harrison grew up in Tuscaloosa, Alabama. On graduating from the

University of Alabama The University of Alabama (informally known as Alabama, UA, or Bama) is a Public university, public research university in Tuscaloosa, Alabama. Established in 1820 and opened to students in 1831, the University of Alabama is the oldest and la ...

, she won a

Marshall Scholarship The Marshall Scholarship is a postgraduate scholarship for "intellectually distinguished young Americans ndtheir country's future leaders" to study at any university in the United Kingdom. It is widely considered one of the most prestigious sc ...

which she used to fund her graduate studies at the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

. She completed her doctorate there in 1975, supervised by

Christopher Zeeman Sir Erik Christopher Zeeman FRS (4 February 1925 – 13 February 2016), was a British mathematician, known for his work in geometric topology and singularity theory. Overview Zeeman's main contributions to mathematics were in topology, partic ...

Hassler Whitney Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes, and geometric integration t ...

was her postdoctoral adviser at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, and she was also one of the

Miller Research Fellows The Miller Research Fellows program is the central program of the Adolph C. and Mary Sprague Miller Institute for Basic Research in Science on the University of California Berkeley campus. The program constitutes the support of Research Fellows - a ...

at Berkeley. She was on the tenured faculty at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

(

Somerville College Somerville College, a constituent college of the University of Oxford in England, was founded in 1879 as Somerville Hall, one of its first two women's colleges. Among its alumnae have been Margaret Thatcher, Indira Gandhi, Dorothy Hodgkin, Ir ...

) 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 Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics facult ...

and

Robion Kirby Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he invented the Kirby–Siebenmann invariant f ...

were the most vocal opponents to her receiving tenure during the case, while

Morris Hirsch Morris William Hirsch (born June 28, 1933) is an American mathematician, formerly at the University of California, Berkeley. A native of Chicago, Illinois, Hirsch attained his doctorate from the University of Chicago in 1958, under supervision of ...

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.
Paul Selvin, Jenny Harrison Finally Gets Tenure in Math at Berkeley, Science 16 Jul 1993: Vol. 261, Issue 5119, pp. 286
Paul Selvin, Does the Harrison Case Reveal Sexism in Math?, Science 28 Jun 1991: Vol. 252, Issue 5014, pp. 1781-1783

Research contributions

Harrison specializes in

geometric analysis Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of l ...

and areas in the intersection of

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, and

geometric measure theory In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfa ...

. She introduced and developed with collaborators a theory of

generalized functions In mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions ...

called

differential chain Differential may refer to: Mathematics * Differential (mathematics) comprises multiple related meanings of the word, both in calculus and differential geometry, such as an infinitesimal change in the value of a function * Differential algebra * ...

sJ. Harrison and H. Pugh, Topological Aspects of Differential Chains, Journal of Geometric Analysis, 22 (2012), no. 3, 685–690 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 Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorpo ...

. The methods apply equally well to domains such as

soap film Soap films are thin layers of liquid (usually water-based) surrounded by air. For example, if two soap bubbles come into contact, they merge and a thin film is created in between. Thus, foams are composed of a network of films connected by Platea ...

fractals In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...

, charged particles, and Whitney stratified spaces, placing them on the same footing as smooth

submanifold In mathematics, a submanifold of a manifold ''M'' is a subset ''S'' which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which p ...

s 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 In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The 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 Jesse Douglas (3 July 1897 – 7 September 1965) was an American mathematician and Fields Medalist known for his general solution to Plateau's problem. Life and career He was born to a Jewish family in New York City, the son of Sarah (née ...

Herbert Federer Herbert Federer (July 23, 1920 – April 21, 2010) was an American mathematician. He is one of the creators of geometric measure theory, at the meeting point of differential geometry and mathematical analysis.Parks, H. (2012''Remembering Herbert ...

and

Wendell Fleming Wendell Helms Fleming (born March 7, 1928) is an American mathematician, specializing in geometrical analysis and stochastic differential equations. Fleming received in 1951 his PhD under Laurence Chisholm Young at the University of Wisconsin� ...

. Recently, she and

Harrison Pugh Harrison may refer to: People * Harrison (name) * Harrison family of Virginia, United States Places In Australia: * Harrison, Australian Capital Territory, suburb in the Canberra district of Gungahlin In Canada: * Inukjuak, Quebec, or " ...

have announced existence and soap film regularity of a solution to a universal Plateau's problem for codimension one surfaces using Hausdorff measure to define area. As a graduate student at the

, where Zeeman introduced her to

. She found a counterexample to the

Seifert conjecture In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit. It is named after Herbert Seifert. In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase ...

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 In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is als ...

of differential chains satisfies a

universal property In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently fro ...

determined by two natural axioms. They have used the theory to provide the first universal solution to

, including soap film regularity, building upon Harrison's earlier paper. Recently, Fried and Seguin have found a broad generalization to

Reynolds transport theorem In differential calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds (1842–1912), is a three-dimensional generalization of the Leibniz int ...

using the methods of differential chains.Eliot Fried and Brian Seguin, Mathematical Models and Methods in Applied Sciences, Vol. 24, No. 9 (2014) 1729–1779

Awards and fellowships

Foundational Questions Institute The Foundational Questions Institute, styled FQXi, is an organization that provides grants to "catalyze, support, and disseminate research on questions at the foundations of physics and cosmology." It was founded in 2005 by cosmologists Max Tegmark ...

, research award, 2009 * Miller Institute for Basic Research in Science, Miller Professor, 2007 *

Rockefeller University The Rockefeller University is a private biomedical research and graduate-only university in New York City, New York. It focuses primarily on the biological and medical sciences and provides doctoral and postdoctoral education. It is classif ...

, Visiting Research Professor, 1996–97 *

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National I ...

, Visiting Scholar, 1989–90 *

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

, CUF Lecturer and Tutorial Fellow,

, 1978–81 * Miller Institute for Basic Research in Science, Miller Fellow, 1977–78 *

, Visiting Fellow, Princeton, 1975–76

References

External links

Harrison's webpage
* {{DEFAULTSORT:Harrison, Jenny Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians University of Alabama alumni Alumni of the University of Warwick Academics of the University of Oxford University of California, Berkeley College of Letters and Science faculty Fellows of Somerville College, Oxford 20th-century women mathematicians 21st-century women mathematicians Year of birth missing (living people) 20th-century American women 21st-century American women