James Eells (October 25, 1926 – February 14, 2007) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, who specialized in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

Biography

Eells studied mathematics at

Bowdoin College Bowdoin College ( ) is a private liberal arts college in Brunswick, Maine. When Bowdoin was chartered in 1794, Maine was still a part of the Commonwealth of Massachusetts. The college offers 34 majors and 36 minors, as well as several joint eng ...

Maine Maine () is a state in the New England and Northeastern regions of the United States. It borders New Hampshire to the west, the Gulf of Maine to the southeast, and the Canadian provinces of New Brunswick and Quebec to the northeast and north ...

and earned his undergraduate degree in 1947. After graduation he spent one year teaching mathematics at

Robert College The American Robert College of Istanbul ( tr, İstanbul Özel Amerikan Robert Lisesi or ), often shortened to Robert, or RC, is a Selective school, highly selective, Independent school, independent, mixed-sex education, co-educational Secondary ...

Istanbul Istanbul ( , ; tr, İstanbul ), formerly known as Constantinople ( grc-gre, Κωνσταντινούπολις; la, Constantinopolis), is the List of largest cities and towns in Turkey, largest city in Turkey, serving as the country's economic, ...

and starting in 1948 was for two years an instructor at

Amherst College Amherst College ( ) is a private liberal arts college in Amherst, Massachusetts. Founded in 1821 as an attempt to relocate Williams College by its then-president Zephaniah Swift Moore, Amherst is the third oldest institution of higher educatio ...

Amherst, Massachusetts Amherst () is a New England town, town in Hampshire County, Massachusetts, United States, in the Connecticut River valley. As of the 2020 census, the population was 39,263, making it the highest populated municipality in Hampshire County (althoug ...

. Next he undertook graduate study at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where in 1954 he received his

Ph.D A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common Academic degree, degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields ...

under

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 ...

with thesis ''Geometric Aspects of Integration Theory''. In the academic year 1955–1956 he was 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 subsequently in 1962–1963, 1972–1973, 1977, and 1982).IAS Member Page: James Eells
/ref> He taught at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

for several years. In 1964 he became a full professor at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

. In 1963 and in 1966–1967 he was at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

, and after a visit to the new mathematics department developed by

Erik 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 ...

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 ...

Eells became a professor of mathematical analysis there in 1969. Eells organized many of the University of Warwick Symposia in mathematics. In 1986 he became the first director of the mathematics section of the

Abdus Salam International Centre for Theoretical Physics The Abdus Salam International Centre for Theoretical Physics (ICTP) is an international research institute for physical and mathematical sciences that operates under a tripartite agreement between the Italian Government, United Nations Education ...

Trieste Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into provi ...

; for six years he served as director in addition to his appointment at the University of Warwick. In 1992 he retired and lived in

Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

. Eells did research on

global analysis In mathematics, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles. Global analysis uses techniques in infinite-dimensional manifold th ...

, especially,

harmonic map In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain nonlinear partial differential equation. This partial differential equation for ...

s on

Riemannian manifold In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real manifold, real, smooth manifold ''M'' equipped with a positive-definite Inner product space, inner product ...

s, which are important in the theory of

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

s and

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

. His doctoral students included John C. Wood. In 1970 he was an invited speaker at the

International Mathematical Congress The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...

(''On Fredholm manifolds'' with K. D. Elworthy). He was co-editor of the collected works of

. Eells's doctoral students include luc LEMAIRE Peter Štefan (1941–1978), Giorgio Valli (1960–1999) and . Eells was married since 1950 and had a son and three daughters.

Publications

* * * *with J. H. Sampson: * *''Singularities of smooth maps'', London, Nelson 1967 *with Luc Lemaire: ; re-published with a follow-up report in the books ''Harmonic Maps'', 1992, and ''Two Reports on Harmonic Maps'', 1994, by publisher World Scientific *with Luc Lemaire: ''Selected topics in harmonic maps'', AMS 1983 *with Andrea Ratto: ''Harmonic maps and minimal immersions with symmetries – methods of ordinary differential equations applied to elliptic variational problems'', Princeton University Press 1993 *with B. Fuglede
''Harmonic maps between Riemannian polyhedra''
Cambridge University Press 2001

References

External links

* * * Toledo, Domingo
James Eells 1926–2007.
Notices Amer. Math. Soc. 55 (2008), no. 6, 704–706. * Chiang, Yuan-Jen; Ratto, Andrea
Paying tribute to James Eells and Joseph H, Sampson: in commemoration of the fiftieth anniversary of their pioneering work on harmonic maps.
Notices Amer. Math. Soc. 62 (2015), no. 4, 388–393. {{DEFAULTSORT:Eells, James 20th-century American mathematicians 1926 births 2007 deaths Bowdoin College alumni Harvard University alumni Amherst College faculty Columbia University faculty Cornell University faculty Academics of the University of Warwick Scientists from Cleveland Mathematicians from Ohio Geometers Mathematical analysts

Biography

Publications

See also

References

External links