Editing Lars Ahlfors

{{Short description|Finnish mathematician (1907–1996)}}
{{More citations needed|date=April 2020}}
{{Infobox scientist
|name              = Lars Ahlfors
|image             = Lars Ahlfors - MFO.jpg
|image_size       = 
|caption           = Lars Ahlfors
|birth_date        = {{birth date|1907|04|18|df=y}}
|birth_place       = [[Helsinki]], [[Grand Duchy of Finland|Finland]]
|death_date        = {{death date and age|1996|10|11|1907|04|18|df=y}}
|death_place       = [[Pittsfield, Massachusetts]], U.S.
|nationality       = Finnish
|field             = [[Mathematics]]
|work_institutions = [[University of Helsinki]]<br>[[ETH Zurich]]<br>[[Harvard University]]
|alma_mater        = [[University of Helsinki]] 
|doctoral_advisor  = [[Ernst Lindelöf]]<br>[[Rolf Nevanlinna]]
|doctoral_students = [[Paul Garabedian]]<br>[[Dale Husemoller]]<br>[[James Allister Jenkins|James A. Jenkins]]<br>[[Albert Marden]] <br>[[Robert Osserman]]<br>[[Henry O. Pollak|Henry Pollak]]<br>[[Halsey Royden]]<br>[[George Springer (mathematician)|George Springer]]
|known_for         = [[Analytic capacity]]<br> [[Riemann surface]]s<br> [[Quasiconformal mapping]]s<br> [[Denjoy-Carleman-Ahlfors theorem]]<br> [[Ahlfors finiteness theorem]] for [[Kleinian group]]s<br> [[Ahlfors theory]]<br> [[Conformal geometry]]<br> [[Geometric function theory]]
|influences        = 
|influenced        = 
|prizes            = [[Fields Medal]] (1936)<br>[[Wihuri International Prize|Wihuri Prize]] (1968)<br>[[Wolf Prize in Mathematics|Wolf Prize]] (1981)<br>[[Leroy P. Steele Prize]] (1982)
}}
'''Lars Valerian Ahlfors''' (18 April 1907 – 11 October 1996) was a Finnish [[mathematician]], remembered for his work in the field of [[Riemann surface]]s and his textbook on [[complex analysis]].

==Background==
Ahlfors was born in [[Helsinki, Finland]].<ref name="Obit">{{cite news |title=Lars V. Ahlfors, Mathematician Who Won First Fields Medal; 89 |url=https://www.newspapers.com/clip/107571003/lars-ahlfors-1907-1996/ |work=The Boston Globe |date=October 17, 1996 |location=Boston, MA |page=87 |accessdate=August 14, 2022 |via=[[Newspapers.com]]}} {{Open access}}</ref><ref name="Obit2">{{cite news |title=Lars Ahlfors, Leading Mathematician in Complex Analysis, Dies at 89 |url=https://www.newspapers.com/clip/107574120/lars-ahlfors-1907-1996/ |work=The Fresno Bee |date=October 23, 1996 |location=Fresno, CA |page=42 |accessdate=August 14, 2022 |via=[[Newspapers.com]]}} {{Open access}}</ref> 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 Finns|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]] from 1924, graduating in 1928 having studied under [[Ernst Lindelöf]] and [[Rolf Nevanlinna]].<ref name="Obit"/> He assisted Nevanlinna in 1929 with his work on [[Denjoy–Carleman–Ahlfors theorem|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.<ref>{{Cite book |last=Ahlfors |first=Lars Valerian |url=https://books.google.com/books?id=CiXWCgAAQBAJ&dq=Denjoy%E2%80%93Carleman%E2%80%93Ahlfors+theorem&pg=PA148 |title=Analytic Functions |date=2015-12-08 |publisher=Princeton University Press |isbn=978-1-4008-7670-9 |language=en}}</ref> 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 [[University of Helsinki]] from 1933 to 1936. In 1936 he was one of the first two people to be awarded the [[Fields Medal]]<ref name="Obit"/><ref name="Obit2"/> (the other was [[Jesse Douglas]]). In 1935 Ahlfors visited [[Harvard University]].<ref name="Obit2"/> He returned to [[Finland]] 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 [[ETH Zurich|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]], so in 1946 he jumped at a chance to leave, returning to work at Harvard, where he remained until his retirement in 1977;<ref name="Obit"/><ref name="Obit2"/> he was William Caspar Graustein Professor of Mathematics from 1964. Ahlfors was a visiting scholar at the [[Institute for Advanced Study]] in 1962 and again in 1966.<ref>[http://www.ias.edu/people/cos/ Institute for Advanced Study: A Community of Scholars]</ref> 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]], 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)<ref>{{cite journal|author=Springer, George|author-link=George Springer (mathematician)|title=Review of ''Riemann surfaces''. By Lars V. Ahlfors and Leo Sario|journal=Bull. Amer. Math. Soc.|volume=67|issue=2|pages=170–171|url=https://www.ams.org/journals/bull/1961-67-02/S0002-9904-1961-10548-X/S0002-9904-1961-10548-X.pdf|doi=10.1090/S0002-9904-1961-10548-X|doi-access=free}}</ref> and ''Conformal invariants'' (1973).
He made decisive contributions to [[meromorphic]] curves, [[value distribution theory]], [[Riemann surface]]s, [[conformal geometry]], [[quasiconformal mapping]]s and other areas during his career.

==Personal life==
In 1933, he married Erna Lehnert, an [[Austrians|Austrian]] who with her parents had first settled in [[Sweden]] and then in [[Finland]]. The couple had three daughters. Ahlfors died of pneumonia at the Willowwood nursing home in [[Pittsfield, Massachusetts]] in 1996.<ref name="Obit"/><ref name="Obit2"/>

==See also==

*[[Ahlfors finiteness theorem]]
*[[Analytic capacity#Ahlfors function|Ahlfors function]]
*[[Ahlfors measure conjecture]]
*[[Grunsky matrix#Beurling transform|Beurling–Ahlfors transform]]
*[[Schwarz–Ahlfors–Pick theorem]]
*[[Measurable Riemann mapping theorem]]

==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; [[Lipman Bers|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. {{ISBN|3-7643-3075-9}}
* 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. {{ISBN|3-7643-3076-7}}
'''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. {{ISBN|0-07-000657-1}}<ref>{{cite journal|author=Schaeffer, A. C.|author-link=Albert Charles Schaeffer|title=Review: ''Complex analysis''. By Lars V. Ahlfors|journal=Bull. Amer. Math. Soc.|year=1953|volume=59|issue=5|pages=464–467|url=https://www.ams.org/journals/bull/1953-59-05/S0002-9904-1953-09722-1/S0002-9904-1953-09722-1.pdf|doi=10.1090/S0002-9904-1953-09722-1|doi-access=free}}</ref>
* 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. {{ISBN|978-0-8218-5270-5}}
* 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. {{ISBN|0-8218-3644-7}}
* 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 ==
{{reflist}}

==External links==
*{{Commons category-inline}}
*{{MathGenealogy |id=1430 }}
* [http://www.math.harvard.edu/history/ahlfors/ Ahlfors] entry on Harvard University Mathematics department web site.
*[http://nrs.harvard.edu/urn-3:HUL.ARCH:hua16002 Papers of Lars Valerian Ahlfors : an inventory] (Harvard University Archives)
*[http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Ahlfors.html Lars Valerian Ahlfors] The MacTutor History of Mathematics page about Ahlfors
*[https://www.ams.org/notices/199802/ahlfors.pdf The Mathematics of Lars Valerian Ahlfors], ''Notices of the American Mathematical Society''; vol. 45, no. 2 (February 1998).
*[https://www.ams.org/notices/199802/comm-krantz.pdf Lars Valerian Ahlfors (1907–1996)], ''Notices of the American Mathematical Society''; vol. 45, no. 2 (February 1998).
*{{cite journal
| url = http://books.nap.edu/html/biomems/lahlfors.pdf
| title = Lars Valerian Ahlfors: a biographical memoir
| author = Frederick Gehring
| journal = Biographical Memoirs
| volume = 87
| year = 2005
}}
*[http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/ahlfors-lars.pdf National Academy of Sciences Biographical Memoir]
*[https://zbmath.org/authors/?q=ai:ahlfors.lars-valerian Author profile] in the database [[Zentralblatt MATH|zbMATH]]
{{Fields medalists}}
{{Wolf Prize in Mathematics}}
{{John von Neumann Lecturers}}
{{Authority control}}

{{DEFAULTSORT:Ahlfors, Lars}}
[[Category:1907 births]]
[[Category:1996 deaths]]
[[Category:20th-century Finnish mathematicians]]
[[Category:Academic staff of the Helsinki University of Technology]]
[[Category:Finnish emigrants to the United States]]
[[Category:Complex analysts]]
[[Category:Fields Medalists]]
[[Category:Foreign members of the Russian Academy of Sciences]]
[[Category:Foreign members of the USSR Academy of Sciences]]
[[Category:Harvard University Department of Mathematics faculty]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Mathematical analysts]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:People from Uusimaa Province (Grand Duchy of Finland)]]
[[Category:People from Winchester, Massachusetts]]
[[Category:Swedish-speaking Finns]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Members of the Royal Swedish Academy of Sciences]]