Jenny Harrison
Encyclopedia
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 was born in Atlanta, Georgia
on February 4, 1949. 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 distribution
s 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.
Geometric analysis
Geometric analysis is a mathematical discipline at the interface of differential geometry and differential equations. It includes both the use of geometrical methods in the study of partial differential equations , and the application of the theory of partial differential equations to geometry...
and areas in the intersection of algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, and geometric measure theory
Geometric measure theory
In mathematics, geometric measure theory is the study of the geometric properties of the measures of sets , including such things as arc lengths and areas. It uses measure theory to generalize differential geometry to surfaces with mild singularities called rectifiable sets...
. 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
Abraham Robinson
Abraham Robinson was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics....
. 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
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 non-existence as a conjecture...
. She has pioneered applications of operator calculus (called chainlet geometry in) to the calculus of variations, physics, and numerical analysis.
Harrison was born in Atlanta, Georgia
Atlanta, Georgia
Atlanta is the capital and most populous city in the U.S. state of Georgia. According to the 2010 census, Atlanta's population is 420,003. Atlanta is the cultural and economic center of the Atlanta metropolitan area, which is home to 5,268,860 people and is the ninth largest metropolitan area in...
on February 4, 1949. Her graduate studies were at the University of Warwick
University of Warwick
The University of Warwick is a public research university located in Coventry, United Kingdom...
where E.C. Zeeman introduced her to Plateau's Problem. Hassler Whitney
Hassler Whitney
Hassler Whitney was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes.-Work:...
was her postdoctoral adviser at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
. After her time at the Institute, she became an instructor at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. 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 distribution
Distribution (mathematics)
In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
s and de Rham currents, settling a question posed by Michael Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
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
Stephen Smale
Steven Smale a.k.a. Steve Smale, Stephen Smale is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley .-Education and career:He entered the University of...
and Robion Kirby
Robion Kirby
Robion Cromwell Kirby is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology...
were the most vocal opponents to her receiving tenure during the case, while Morris Hirsch and James Yorke
James Yorke
James Yorke may refer to:* James A. Yorke, mathematician* James Yorke *James Yorke -See also:*James Yorke Scarlett, British general in the Crimea War*James York...
were her most vocal supporters.
Awards and Fellowships
- Foundational Questions InstituteFoundational Questions InstituteThe Foundational Questions Institute, styled FQXi, is an organization which provides grants to “catalyze, support, and disseminate research on questions at the foundations of physics and cosmology.” It has run two worldwide grant competitions....
, research award, 2009 - Miller Institute for Basic Research in Science, Miller Professor, 2007
- Rockefeller UniversityRockefeller UniversityThe Rockefeller University is a private university offering postgraduate and postdoctoral education. It has a strong concentration in the biological sciences. It is also known for producing numerous Nobel laureates...
, Visiting Research Professor, 1996–97 - Yale UniversityYale UniversityYale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
, National Science FoundationNational Science FoundationThe National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
, Visiting Scholar, 1989–90 - Various NSF and DARPA grants in the 1980s
- Oxford University, Tutorial Fellow, Somerville College, 1978–81
- Miller Institute for Basic Research in Science, Miller Fellow, 1977–78
- Institute for Advanced StudyInstitute for Advanced StudyThe Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
, Visiting Fellow, Princeton, 1975–76 - In 1971 she was awarded the first Marshall ScholarshipMarshall ScholarshipThe Marshall Scholarship, a postgraduate scholarships available to Americans, was created by the Parliament of the United Kingdom when the Marshall Aid Commemoration Act was passed in 1953. The scholarships serve as a living gift to the United States of America in recognition of the post-World War...
to a student from the University of AlabamaUniversity of AlabamaThe University of Alabama is a public coeducational university located in Tuscaloosa, Alabama, United States....
where her studies were primarily in music. The funds supported her studies in mathematics at the University of WarwickUniversity of WarwickThe University of Warwick is a public research university located in Coventry, United Kingdom...
.
Selected works
- Unsmoothable diffeomorphisms. Annals of MathematicsAnnals of MathematicsThe Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
, vol. 102, pp. 85–94, 1975. - Stokes' theorem for nonsmooth chains. Bulletin of the American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, October, 1993. -
counterexamples to the Seifert conjecture. TopologyTopology (journal)Topology is a mathematical journal publishing scholarly articles related to topology and geometry. It was founded by J. H. C. Whitehead in 1962 and is published by Elsevier....
, vol. 27, no. 3, pp. 249–278, 1988.
External links
- Harrison's webpage - information on her life, career, research, and lawsuit