{{Short description|American mathematician (1926–2007)}} {{Use mdy dates|date=October 2012}} {{Infobox scientist | name = James Eells | image = James Eells (left) and Nicolaas Kuiper at the Chern Symposium 1979 in Berkeley.jpg <!--(filename only, i.e. without "File:" prefix)--> | image_size = | image_upright = | alt = | caption = James Eells (left) and Nicolaas Kuiper (right) at the 1979 Chern Symposium in Berkeley, California | birth_date = {{birth date |1926|10|25|mf=yes}} | birth_place = Cleveland, Ohio | spouse = Anna Eells | death_date = {{death date and age |2007|2|14 |1926|10|25}} | death_place = Cambridge, UK | fields = Mathematics | workplaces = | alma_mater = | thesis_title = Geometric Aspects of Integration Theory | thesis_url = http://id.lib.harvard.edu/alma/990038430660203941/catalog | thesis_year = 1954 | doctoral_advisor = Hassler Whitney | doctoral_students = John C. Wood | known_for = Harmonic maps | awards = }} '''James Eells''' (October 25, 1926 &ndash; February 14, 2007) was an American mathematician, who specialized in mathematical analysis.

==Biography== Eells was born on 25 October 1926, in Cleveland, Ohio.<ref>{{cite journal |last1=Toledo |first1=Domingo |title=James Eells: 1926–2007 |journal=Notices of the American Mathematical Society |date=June 2008 |volume=55 |issue=6 |pages=704–706 |url=https://www.ams.org/notices/200806/tx080600704p.pdf |access-date=11 February 2024}}</ref> Eells studied mathematics at Bowdoin College in Maine and earned his undergraduate degree in 1947. After graduation he spent one year teaching mathematics at Robert College in Istanbul and starting in 1948 was for two years an instructor at Amherst College in Amherst, Massachusetts. Next he undertook graduate study at Harvard University, where in 1954 he received his Ph.D. under Hassler Whitney with thesis ''Geometric Aspects of Integration Theory''.

In the academic year 1955–1956 he was at the Institute for Advanced Study (and subsequently in 1962–1963, 1972–1973, 1977, and 1982).<ref>[https://www.ias.edu/scholars/james-eells IAS Member Page: James Eells]</ref> He taught at Columbia University for several years. In 1964 he became a full professor at Cornell University. In 1963 and in 1966–1967 he was at the University of Cambridge, and after a visit to the new mathematics department developed by Erik Christopher Zeeman at the University of Warwick 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 in Trieste; 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.

Eells did research on global analysis, especially, harmonic maps on Riemannian manifolds, which are important in the theory of minimal surfaces and theoretical physics. His doctoral students included John C. Wood.

In 1970 he was an invited speaker at the International Mathematical Congress in Nice (''On Fredholm manifolds'' with K. D. Elworthy).

He was co-editor of the collected works of Hassler Whitney. Eells's doctoral students include Luc Lemaire, Peter Štefan (1941–1978), Giorgio Valli (1960–1999) and {{Interlanguage link multi|Pierre de la Harpe|de}}. Eells was married since 1950 and had a son and three daughters.

==Publications== * {{cite journal|last= Eells|first= James| title=Geometric aspects of currents and distributions|journal=Proceedings of the National Academy of Sciences of the United States of America |year=1955|volume=41|issue=7|pages=493–496|pmc=528123|doi=10.1073/pnas.41.7.493|pmid=16589704|bibcode= 1955PNAS...41..493E|doi-access= free}} * {{cite journal|last= Eells|first= James| title=On submanifolds of certain function spaces|journal=Proceedings of the National Academy of Sciences of the United States of America|year=1959|volume=45|issue=10|pages=1520–1522|pmc=222748|doi=10.1073/pnas.45.10.1520|pmid=16590536|bibcode= 1959PNAS...45.1520E|doi-access= free}} * {{cite journal| mr=0212840|last1=Earle|first1= Clifford J.|author1-link=Clifford John Earle Jr.| last2= Eells|first2= James| title=The diffeomorphism group of a compact Riemann surface| journal=Bulletin of the American Mathematical Society | volume=73|year=1967|issue=4|pages=557–559|doi=10.1090/S0002-9904-1967-11746-4|doi-access=free}} *with J. H. Sampson: {{cite journal|title=Harmonic Mappings of Riemannian Manifolds|journal=American Journal of Mathematics |year=1964|volume=86|pages=109–160|doi=10.2307/2373037|jstor=2373037 |last1=Eells |first1=James |last2=Sampson |first2=J. H. |issue=1 }} * {{cite journal|title=A setting for global analysis|journal=Bulletin of the American Mathematical Society |year=1966|volume=72|issue=5|pages=751–807|mr=0203742|doi=10.1090/S0002-9904-1966-11558-6|doi-access=free|last1=Eells Jr |first1=James }} *''Singularities of smooth maps'', London, Nelson 1967 *with Luc Lemaire: {{cite journal|title=A report on harmonic maps|journal=Bulletin of the London Mathematical Society|year=1978|volume=10|pages=1–68|doi=10.1112/blms/10.1.1|last1=Eells|first1=J.|last2=Lemaire|first2=L.}}; 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: [https://books.google.com/books/about/Harmonic_Maps_Between_Riemannian_Polyhed.html?id=8pjRqy5EfoEC ''Harmonic maps between Riemannian polyhedra''], Cambridge University Press 2001

==See also== *Eells–Kuiper manifold

==References== {{reflist}}

==External links== *{{MacTutor Biography|id=Eells}} *{{MathGenealogy|id=19865}} * Toledo, Domingo. [https://www.ams.org/journals/notices/200806/tx080600704p.pdf James Eells 1926–2007.] Notices Amer. Math. Soc. 55 (2008), no. 6, 704–706. * Chiang, Yuan-Jen; Ratto, Andrea. [https://www.ams.org/notices/201504/rnoti-p388.pdf 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. {{Authority control}}

{{DEFAULTSORT:Eells, James}} Category:20th-century American mathematicians Category:1926 births Category:2007 deaths Category:Bowdoin College alumni Category:Harvard University alumni Category:Amherst College faculty Category:Columbia University faculty Category:Cornell University faculty Category:Academics of the University of Warwick Category:Scientists from Cleveland Category:Mathematicians from Ohio Category:American geometers Category:American mathematical analysts