Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish

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, mathematical structure, structure, space, Mathematica ...

, remembered for his work in the field of Riemann surfaces and his textbook on

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

Background

Ahlfors was born in Helsinki, Finland. His mother, Sievä Helander, died at his birth. His father, Axel Ahlfors, was a professor of engineering at the Helsinki University of Technology. The Ahlfors family was Swedish-speaking, so he first attended the private school Nya svenska samskolan where all classes were taught in Swedish. Ahlfors studied at

University of Helsinki The University of Helsinki (, ; UH) is a public university in Helsinki, Finland. The university was founded in Turku in 1640 as the Royal Academy of Åbo under the Swedish Empire, and moved to Helsinki in 1828 under the sponsorship of Alexander ...

from 1924, graduating in 1928 having studied under Ernst Lindelöf and Rolf Nevanlinna. He assisted Nevanlinna in 1929 with his work on Denjoy's conjecture on the number of asymptotic values of an entire function. In 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem. It states that the number of asymptotic values approached by an entire function of order ρ along curves in the complex plane going toward infinity is less than or equal to 2ρ. He completed his doctorate from the University of Helsinki in 1930.

Career

Ahlfors worked as an associate professor at the

from 1933 to 1936. In 1936 he was one of the first two people to be awarded the Fields Medal (the other was Jesse Douglas). In 1935 Ahlfors visited

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

. He returned to

Finland Finland, officially the Republic of Finland, is a Nordic country in Northern Europe. It borders Sweden to the northwest, Norway to the north, and Russia to the east, with the Gulf of Bothnia to the west and the Gulf of Finland to the south, ...

in 1938 to take up a professorship at the University of Helsinki. The outbreak of war in 1939 led to problems although Ahlfors was unfit for military service. He was offered a position at the Swiss Federal Institute of Technology at Zurich in 1944 and finally managed to travel there in March 1945. He did not enjoy his time in

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

, so in 1946 he jumped at a chance to leave, returning to work at Harvard, where he remained until his retirement in 1977; he was William Caspar Graustein Professor of Mathematics from 1964. Ahlfors was a visiting scholar 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 ...

in 1962 and again in 1966. He was awarded the Wihuri Prize in 1968 and the Wolf Prize in Mathematics in 1981. He served as the Honorary President of the International Congress of Mathematicians in 1986 at

Berkeley, California Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Anglo-Irish bishop and philosopher George Berkeley. It borders the cities of Oakland, Cali ...

, in celebration of his 50th year of the award of his Fields Medal. His book ''Complex Analysis'' (1953) is the classic text on the subject and is almost certainly referenced in any more recent text which makes heavy use of complex analysis. Ahlfors wrote several other significant books, including ''Riemann surfaces'' (1960) and ''Conformal invariants'' (1973). He made decisive contributions to meromorphic curves, value distribution theory, Riemann surfaces, conformal geometry, quasiconformal mappings and other areas during his career.

Personal life

In 1933, he married Erna Lehnert, an Austrian who with her parents had first settled in

Sweden Sweden, formally the Kingdom of Sweden, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, and Finland to the east. At , Sweden is the largest Nordic count ...

and then in

. The couple had three daughters. Ahlfors died of pneumonia at the Willowwood nursing home in Pittsfield, Massachusetts in 1996.

Bibliography

Articles * Ahlfors, Lars V. ''An extension of Schwarz's lemma.'' Trans. Amer. Math. Soc. 43 (1938), no. 3, 359–364. doi:10.2307/1990065 * Ahlfors, Lars; Beurling, Arne. ''Conformal invariants and function-theoretic null-sets.'' Acta Math. 83 (1950), 101–129. doi:10.1007/BF02392634 * Beurling, A.; Ahlfors, L. ''The boundary correspondence under quasiconformal mappings.'' Acta Math. 96 (1956), 125–142. doi:10.1007/BF02392360 * Ahlfors, Lars; Bers, Lipman. ''Riemann's mapping theorem for variable metrics.'' Ann. of Math. (2) 72 (1960), 385–404. doi:10.2307/1970141 * Ahlfors, Lars Valerian. ''Collected papers. Vol. 1. 1929–1955.'' Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhäuser, Boston, Mass., 1982. xix+520 pp. * Ahlfors, Lars Valerian. ''Collected papers. Vol. 2. 1954–1979.'' Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhäuser, Boston, Mass., 1982. xix+515 pp. Books * Ahlfors, Lars V. ''Complex analysis. An introduction to the theory of analytic functions of one complex variable.'' Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, 1978. xi+331 pp. * Ahlfors, Lars V. ''Conformal invariants. Topics in geometric function theory.'' Reprint of the 1973 original. With a foreword by Peter Duren, F. W. Gehring and Brad Osgood. AMS Chelsea Publishing, Providence, RI, 2010. xii+162 pp. * Ahlfors, Lars V. ''Lectures on quasiconformal mappings.'' Second edition. With supplemental chapters by C. J. Earle, I. Kra, M. Shishikura and J. H. Hubbard. University Lecture Series, 38. American Mathematical Society, Providence, RI, 2006. viii+162 pp. * Ahlfors, Lars V. ''Möbius transformations in several dimensions.'' Ordway Professorship Lectures in Mathematics. University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. ii+150 pp. * Ahlfors, Lars V.; Sario, Leo. ''Riemann surfaces.'' Princeton Mathematical Series, No. 26 Princeton University Press, Princeton, N.J. 1960 xi+382 pp.

References

External links

* *
Ahlfors
entry on Harvard University Mathematics department web site.
Papers of Lars Valerian Ahlfors : an inventory
(Harvard University Archives)

The MacTutor History of Mathematics page about Ahlfors
The Mathematics of Lars Valerian Ahlfors
''Notices of the American Mathematical Society''; vol. 45, no. 2 (February 1998).
Lars Valerian Ahlfors (1907–1996)
''Notices of the American Mathematical Society''; vol. 45, no. 2 (February 1998). *
National Academy of Sciences Biographical MemoirAuthor profile
in the database zbMATH {{DEFAULTSORT:Ahlfors, Lars 1907 births 1996 deaths 20th-century Finnish mathematicians Academic staff of the Helsinki University of Technology Finnish emigrants to the United States Complex analysts Fields Medalists Foreign members of the Russian Academy of Sciences Foreign members of the USSR Academy of Sciences Harvard University Department of Mathematics faculty Institute for Advanced Study visiting scholars Mathematical analysts Members of the United States National Academy of Sciences People from Uusimaa Province (Grand Duchy of Finland) People from Winchester, Massachusetts Swedish-speaking Finns Wolf Prize in Mathematics laureates Members of the Royal Swedish Academy of Sciences