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 university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

Education and early career

Harrison grew up in Tuscaloosa, Alabama, and earned her undergraduate degree from the

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

. Awarded 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 considered among the most prestigious scholarsh ...

, she pursued 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 and Warwickshire, England. The university was founded in 1965 as part of ...

. While at Warwick, Harrison produced a counterexample to a conjecture of

Arnaud Denjoy Arnaud Denjoy (; 5 January 1884 – 21 January 1974) was a French mathematician. Biography Denjoy was born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to ...

(a similar one was discovered independently by

Charles Fefferman Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contribu ...

and

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...

) which was published in the

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

in 1975. She completed her PhD that same year under the supervision of

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, immersion (mathematics), immersions, characteristic classes and, ...

was Harrison's postdoctoral adviser at the

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

, and she was also one of the

Miller Research Fellows The Miller Institute for Basic Research in Science was established on the University of California, Berkeley, campus in 1955 after Adolph C. Miller and his wife, Mary Sprague Miller, made a donation to the university. It was their wish that the do ...

Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California *George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer to ...

. She was on the tenured faculty at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

(

Somerville College Somerville College is a constituent college of the University of Oxford in England. It was founded in 1879 as Somerville Hall, one of its first two women's colleges. It began admitting men in 1994. The college's liberal tone derives from its f ...

) from 1978 to 1981, before returning to Berkeley as an assistant professor. In 1986, after being denied tenure, Harrison filed a lawsuit alleging gender discrimination. The case drew national attention within the academic community. A 1993 settlement led to a new review of her research by an independent panel of seven mathematicians and scientists, who unanimously recommended her promotion to full professor.

Later career

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 ...

and areas in the intersection of

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, 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 surfac ...

. She introduced and developed with collaborators a theory of

generalized functions In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful for tr ...

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 reincorp ...

. 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 Plat ...

fractals In mathematics, a fractal is a Shape, 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 scale ...

, 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 S \rightarrow M satisfies certain properties. There are different types of submanifolds depending on exactly ...

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 (July 3, 1897 – September 7, 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 ...

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 F ...

and

Wendell Fleming Wendell Helms Fleming (March 7, 1928 – February 18, 2023) was an American mathematician, specializing in geometrical analysis and stochastic differential equations. Fleming received his PhD in 1951 under Laurence Chisholm Young at the Unive ...

. While a graduate student at the

, Zeeman introduced Harrison 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 n ...

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 used the theory to provide the first universal solution to

, including soap film regularity, building upon Harrison's earlier paper.Jenny Harrison, Journal of Geometric Analysis, January 2013, 24(1):271-297

Awards and fellowships

Foundational Questions Institute The Foundational Questions Institute, styled FQxI (formerly 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 cosmolog ...

, research award, 2009 *

Miller Institute for Basic Research in Science The Miller Institute for Basic Research in Science was established on the University of California, Berkeley, campus in 1955 after Adolph C. Miller and his wife, Mary Sprague Miller, made a donation to the university. It was their wish that the d ...

, Miller Professor, 2007 *

Rockefeller University The Rockefeller University is a Private university, private Medical research, biomedical Research university, research and graduate-only university in New York City, New York. It focuses primarily on the biological and medical sciences and pro ...

, Visiting Research Professor, 1996–97 *

Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

, Visiting Scholar, 1989–90 *

Oxford University The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...

, CUF Lecturer and Tutorial Fellow,

, 1978–81 *

, Miller Fellow, 1977–78 *

, Visiting Fellow, Princeton, 1975–76

References

External links

Jenny Harrison
at

* {{DEFAULTSORT:Harrison, Jenny Living people 20th-century American mathematicians 21st-century American 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 American women mathematicians 21st-century American women mathematicians Year of birth missing (living people) Mathematicians from Alabama