View source for Frederick J. Almgren Jr.

{{short description|American mathematician (1933&ndash;1997)}}
{{Infobox scientist
| name              = Frederick Justin Almgren
| image             = <!--(filename only)-->
| alt               =
| caption           = 
| birth_date        = {{Birth date|1933|07|03|mf=y}}
| birth_place       = [[Birmingham, Alabama]], U.S.
| death_date        = {{Death date and age|1997|02|05|1933|07|03|mf=y}}
| death_place       = [[Princeton, New Jersey]], U.S.
| residence         = 
| fields            = [[Geometric measure theory]]
| workplaces        = [[Princeton University]]
| alma_mater        = [[Brown University]]
| thesis_title      = The Homotopy Groups of the Integral Cycle Groups
| thesis_url        = https://search.worldcat.org/title/22016723
| thesis_year       = 1962
| doctoral_advisor  = [[Herbert Federer]]
| academic_advisors = 
| doctoral_students = 
| notable_students  = {{plainlist|1=
*[[Robert V. Kohn]]
*[[Frank Morgan (mathematician)|Frank Morgan]]
*[[Harold R. Parks]]
*[[Jon T. Pitts]]
*[[John M. Sullivan (mathematician)|John M. Sullivan]]
*[[Jean Taylor]]
*[[Brian White (mathematician)|Brian White]]
}}
| known_for         = [[Plateau's problem]], [[Varifold|theory of varifolds]], [[Almgren–Pitts min-max theory]]
| awards            = [[Guggenheim Fellowship]] (1974)
| signature         = <!--(filename only)-->
| signature_alt     = 
| footnotes         = 
| spouse            = [[Jean Taylor]] 
}}
'''Frederick Justin Almgren Jr.''' (July 3, 1933 – February 5, 1997) was an American [[mathematician]] working in [[geometric measure theory]]. He was born in Birmingham, Alabama.

Almgren received a [[Guggenheim Fellowship]] in 1974.  Between 1963 and 1992 he was a frequent visiting scholar at the [[Institute for Advanced Study]] in Princeton.<ref>According to [[#{{harvid|The Institute for Advanced Study|2012}}|Almgren's Community of Scholars web site Profile]] and to {{harv|Mitchell|1980|p=48}}: the latter reference lists his appointments at the Institute only up to 1978.</ref>

Almgren wrote one of the longest papers in mathematics,<ref>Published in book form as {{harv|Almgren|2000}}.</ref> proving what is now called the [[Almgren regularity theorem]]: the singular set of an ''m''-dimensional mass-minimizing surface has dimension at most ''m−2''. He also developed the concept of [[varifold]],<ref>See his mimeographed notes {{harv|Almgren|1964}} and his book {{harv|Almgren|1966}}: the former one is the first exposition of his ideas, but the book (in both its first and second editions {{harv|Almgren|2001}}) had and still has a wider circulation.</ref> first defined by [[Laurence Chisholm Young|L. C. Young]] in {{harv|Young|1951}},<ref>Young calls these geometric objects ''generalized surfaces'': in his commemorative papers describing the research of Almgren, {{harvs|txt|first1=Brian|last1=White|author1-link= Brian White (mathematician)|year=1997|year2=1998|loc1=p.1452, footnote 1|loc2=p.682, footnote 1}} writes that these are "''essentially the same class of surfaces''".</ref> and proposed them as [[generalized solution]]s to [[Plateau's problem]] in order to deal with the problem even when a concept of [[Orientation (geometry)|orientation]] is missing. He played also an important role in the founding of ''[[The Geometry Center]]''.

Almgren was a student of [[Herbert Federer]], one of the founders of [[geometric measure theory]], and was the advisor and husband (as his second wife) of [[Jean Taylor]].
His daughter, [[Ann S. Almgren]], is an applied mathematician who works on computational simulations in astrophysics. His son, [[Robert Almgren|Robert F. Almgren]], is an applied mathematician working on market microstructure and trade execution.

Almgren died in Princeton, New Jersey on February 5, 1997, aged 63.

==Selected publications==
*{{Citation
  | last = Almgren
  | first = Frederick J. Jr.
  | title = The theory of varifolds: A variational calculus in the large for the <math>k</math>-dimensional area integrand
  | place = [[Princeton, New Jersey|Princeton]]
  | publisher = [[Institute for Advanced Study]]
  | year = 1964
}}. A set of [[mimeograph]]ed notes in which Frederick J. Almgren Jr. introduces the term "''varifold''" for the first time. 
*{{Citation
  | last = Almgren
  | first = Frederick J. Jr.
  | title = Plateau's Problem: An Invitation to Varifold Geometry
  | place = New York–Amsterdam
  | publisher = W. A. Benjamin, Inc.
  | series = Mathematics Monographs Series
  | year = 1966
  | edition = 1st
  | pages = XII+74
  | mr = 0190856 
  | zbl = 0165.13201
}}. The first widely circulated book describing the concept of a varifold and its applications to the [[Plateau's problem]].
*{{Citation
| last=Almgren 
| first=Frederick J. Jr. 
| editor-last = Taylor
| editor-first = Jean E.
| editor-link = Jean E. Taylor
| title=Selected works of Frederick J. Almgren, Jr. 
| url=https://books.google.com/books?isbn=0821810677 
| publisher=[[American Mathematical Society]] 
| place=Providence, R.I. 
| series=Collected Works 
| isbn=978-0-8218-1067-5 
| year=1999 
| volume=13 
| mr=1747253 
| zbl=0966.01031 }}.
*{{Citation
| last1=Almgren 
| first1=Frederick J. Jr. 
| editor1-last=Taylor 
| editor1-first=Jean E. 
| editor1-link= Jean Taylor
| editor2-last=Scheffer 
| editor2-first=Vladimir 
| editor2-link= Vladimir Scheffer
| title=Almgren's big regularity paper. Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2 
| url=https://books.google.com/books?isbn=9810241089 
| publisher= [[World Scientific|World Scientific Publishing Co. Inc.]] 
| location=River Edge, NJ 
| series=World Scientific Monograph Series in Mathematics 
| isbn=978-981-02-4108-7 
| year=2000 
| volume=1 
| mr=1777737
| zbl= 0985.49001}}.
*{{Citation
  | last = Almgren
  | first = Frederick J. Jr.
  | author-link = Frederick J. Almgren Jr. 
  | title = Plateau's Problem: An Invitation to Varifold Geometry
  | place = [[Providence, RI]]
  | publisher = [[American Mathematical Society]]
  | series = Student Mathematical Library
  | volume = 13
  | orig-year = 1966
  | year = 2001
  | edition = 2nd
  | pages = xvi, 78
  | url = https://books.google.com/books?id=Tk8zHPGVmBsC
  | isbn = 978-0-8218-2747-5
  | mr = 1853442
  | zbl = 0995.49001 
}}. The second edition of the book {{harv|Almgren|1966}}.

==Notes==
{{reflist|30em}}

==References==

===Biographical references===
*{{Citation
 | editor-last = Mitchell
 | editor-first = Janet A.
 | title = A Community of Scholars. Faculty and Members 1930-1980
 | place = Princeton, New Jersey
 | publisher = The Institute for Advanced Study
 | year = 1980
 | pages = xxii+565
 | url = http://library.ias.edu/files/pdfs/hs/cos.pdf
 | access-date = 2015-07-04
 | archive-date = 2017-11-07
 | archive-url = https://web.archive.org/web/20171107021042/https://library.ias.edu/files/pdfs/hs/cos.pdf
 | url-status = dead
 }}.
*{{Citation
  | last = The New York Times
  | first = Obituary
  | title = Frederick J. Almgren Jr., 63, Math Professor
  | newspaper = [[The New York Times]]
  | date = February 8, 1997
  | url = https://www.nytimes.com/1997/02/08/nyregion/frederick-j-almgren-jr-63-math-professor.html
  | access-date = June 20, 2011}}.
*{{Citation
 | last = The Institute for Advanced Study
 | author-link = Institute for Advanced Study
 | contribution = Almgren, Frederick J. Jr.
 | contribution-url =  http://www.ias.edu/people/cos/users/falmgren01
 | title = A Community of Scholars
 | year = 2012
 | url = http://www.ias.edu/people/cos/
 | access-date = 4 July 2015
}}.

===General references===
*{{Citation
  | last1 = Lieb
  | first1 = Elliott H.
  | author-link = Elliott Lieb
  | last2 = Taylor
  | first2 = Jean
  | author2-link = Jean Taylor
  | last3 = Morgan
  | first3 = Frank
  | author3-link = Frank Morgan (mathematician)
  | last4 = Sullivan
  | first4 = John
  | last5 = Almgren
  | first5 = Robert
  | last6 = Kusner
  | first6 = Robert
  | author6-link = Robert B. Kusner
  | last7 = Marden
  | first7 = Albert
  | author7-link = Albert Marden
  | editor-last = Epstein
  | editor-first = David
  | editor-link= David B. A. Epstein
  | title = In Memoriam Frederick J. Almgren Jr., 1933–1997 
  | journal = [[Experimental Mathematics (journal)|Experimental Mathematics]]
  | volume = 6
  | issue = 1
  | pages = 1–12
  | year = 1997
  | doi = 10.1080/10586458.1997.10504341
 | url = http://www.emis.de/journals/EM/restricted/6/6.1/almgren.ps
  | mr = 1464578
  | zbl = 0883.01029 
}}.
*{{Citation
| last1=Mackenzie 
| first1=Dana 
| author1-link=Dana Mackenzie 
| title=Fred Almgren (1933–1997): lover of mathematics, family, and life's adventures 
| url=https://www.ams.org/notices/199709/index.html 
| year=1997 
| journal=[[Notices of the American Mathematical Society]] 
| issn=0002-9920 
| volume=44 
| issue=9 
| pages=1102–1106 
| mr=1470170 
| zbl = 0908.01016}}.
*{{Citation
| last1 = White
| first1 = Brian 
| author1-link = Brian White (mathematician)
| title = The Mathematics of F. J. Almgren Jr.
| url = https://www.ams.org/notices/199711/index.html
| year = 1997 
| journal = [[Notices of the American Mathematical Society]] 
| issn = 0002-9920 
| volume = 44 
| issue = 11 
| pages = 1451–1456 
| mr = 1488574
| zbl = 0908.01017
}}.
*{{Citation
 | last=White
 | first=Brian
 | title=The mathematics of F. J. Almgren, Jr.
 | year=1998
 | journal=[[The Journal of Geometric Analysis]]
 | issn=1050-6926
 | volume=8
 | issue=5
 | pages=681–702
 | doi=10.1007/BF02922665
 | mr=1731057
 | zbl=0955.01020
| s2cid=122083638
 }}.

===Scientific references===
*{{Citation
  | last = Young
  | first = L. C.
  | author-link = Laurence Chisholm Young
  | title = Surfaces paramétriques généralisées
  | journal = [[Bulletin de la Société Mathématique de France]]
  | volume = 79
  | pages = 59–84
  | year=1951
  | doi = 10.24033/bsmf.1419
 | url =http://www.numdam.org/item?id=BSMF_1951__79__59_0
  | mr = 46421
  | zbl = 0044.10203
| doi-access = free
  }}.
*{{Citation
  | first = Ennio
  | last = De Giorgi
  | author-link = Ennio De Giorgi
  | editor-last = Petrovsky
  | editor-first = I. G.
  | editor-link = Ivan Petrovsky
  | contribution = Hypersurfaces of minimal measure in pluridimensional euclidean spaces
  | contribution-url = http://www.mathunion.org/ICM/ICM1966.1/Main/icm1966.1.0395.0401.ocr.pdf
  | series = [[International Congress of Mathematicians|ICM Proceedings]]
  | title = Trudy Mezhdunarodnogo kongressa matematikov. Proceedings of International Congress of Mathematicians (Moscow−1966)
  | year = 1968
  | pages = 395−401
  | place = [[Moscow]]
  | publisher = [[Mir Publishers]]
  | url = http://www.mathunion.org/ICM/ICM1966.1/
  | mr = 0234329
  | zbl = 0188.17503
  | access-date = 2015-07-04
  | archive-date = 2015-07-06
  | archive-url = https://web.archive.org/web/20150706164436/http://www.mathunion.org/ICM/ICM1966.1/
  | url-status = dead
  }}.

==See also==
*[[Almgren regularity theorem]]
*[[Almgren–Pitts min-max theory]]
*[[Almgren Isomorphism Theorem]]

==External links==
*{{MacTutor Biography|id=Almgren}}
*{{MathGenealogy|id=4367}}

{{Authority control}}

{{DEFAULTSORT:Almgren, Frederick}}
[[Category:1933 births]]
[[Category:1997 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Princeton University faculty]]
[[Category:Mathematicians from Alabama]]
[[Category:People from Birmingham, Alabama]]