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Frederick J. Almgren Jr.

August 21, 2023

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.

Frederick Justin Almgren
Born(1933-07-03)July 3, 1933
Birmingham, Alabama, U.S.
DiedFebruary 5, 1997(1997-02-05) (aged 63)
Princeton, New Jersey, U.S.
NationalityAmerican
Alma materBrown University
Known forPlateau's problem, theory of varifolds, Almgren–Pitts min-max theory
SpouseJean Taylor
AwardsGuggenheim Fellowship (1974)
Scientific career
FieldsGeometric measure theory
InstitutionsPrinceton University
Doctoral advisorHerbert Federer
Notable students
InfluencedGeometric measure theory

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.[1]

Almgren wrote one of the longest papers in mathematics,[2] 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,[3] first defined by L. C. Young in (Young 1951),[4] and proposed them as generalized solutions to Plateau's problem in order to deal with the problem even when a concept of 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 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

  • Almgren, Frederick J. Jr. (1964), The theory of varifolds: A variational calculus in the large for the  -dimensional area integrand, Princeton: Institute for Advanced Study. A set of mimeographed notes in which Frederick J. Almgren Jr. introduces the term "varifold" for the first time.
  • Almgren, Frederick J. Jr. (1966), Plateau's Problem: An Invitation to Varifold Geometry, Mathematics Monographs Series (1st ed.), New York–Amsterdam: W. A. Benjamin, Inc., pp. 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.
  • Almgren, Frederick J. Jr. (1999), Taylor, Jean E. (ed.), Selected works of Frederick J. Almgren, Jr., Collected Works, vol. 13, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1067-5, MR 1747253, Zbl 0966.01031.
  • Almgren, Frederick J. Jr. (2000), Taylor, Jean E.; Scheffer, Vladimir (eds.), Almgren's big regularity paper. Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2, World Scientific Monograph Series in Mathematics, vol. 1, River Edge, NJ: World Scientific Publishing Co. Inc., ISBN 978-981-02-4108-7, MR 1777737, Zbl 0985.49001.
  • Almgren, Frederick J. Jr. (2001) [1966], Plateau's Problem: An Invitation to Varifold Geometry, Student Mathematical Library, vol. 13 (2nd ed.), Providence, RI: American Mathematical Society, pp. xvi, 78, ISBN 978-0-8218-2747-5, MR 1853442, Zbl 0995.49001. The second edition of the book (Almgren 1966).

Notes

  1. ^ According to Almgren's Community of Scholars web site Profile and to (Mitchell 1980, p. 48): the latter reference lists his appointments at the Institute only up to 1978.
  2. ^ Published in book form as (Almgren 2000).
  3. ^ See his mimeographed notes (Almgren 1964) and his book (Almgren 1966): the former one is the first exposition of his ideas, but the book (in both its first and second editions (Almgren 2001)) had and still has a wider circulation.
  4. ^ Young calls these geometric objects generalized surfaces: in his commemorative papers describing the research of Almgren, Brian White (1997, p.1452, footnote 1, 1998, p.682, footnote 1) writes that these are "essentially the same class of surfaces".

References

Biographical references

  • Mitchell, Janet A., ed. (1980), (PDF), Princeton, New Jersey: The Institute for Advanced Study, pp. xxii+565, archived from the original (PDF) on 2017-11-07, retrieved 2015-07-04.
  • The New York Times, Obituary (February 8, 1997), "Frederick J. Almgren Jr., 63, Math Professor", The New York Times, retrieved June 20, 2011.
  • The Institute for Advanced Study (2012), "Almgren, Frederick J. Jr.", A Community of Scholars, retrieved 4 July 2015.

General references

Scientific references

See also

External links

August 21, 2023
frederick, almgren, frederick, justin, almgren, july, 1933, february, 1997, american, mathematician, working, geometric, measure, theory, born, birmingham, alabama, frederick, justin, almgrenborn, 1933, july, 1933birmingham, alabama, diedfebruary, 1997, 1997, . 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 Frederick Justin AlmgrenBorn 1933 07 03 July 3 1933Birmingham Alabama U S DiedFebruary 5 1997 1997 02 05 aged 63 Princeton New Jersey U S NationalityAmericanAlma materBrown UniversityKnown forPlateau s problem theory of varifolds Almgren Pitts min max theorySpouseJean TaylorAwardsGuggenheim Fellowship 1974 Scientific careerFieldsGeometric measure theoryInstitutionsPrinceton UniversityDoctoral advisorHerbert FedererNotable studentsRobert V Kohn Frank Morgan Harold R Parks Jon T Pitts John M Sullivan Jean Taylor Brian WhiteInfluencedGeometric measure theoryAlmgren received a Guggenheim Fellowship in 1974 Between 1963 and 1992 he was a frequent visiting scholar at the Institute for Advanced Study in Princeton 1 Almgren wrote one of the longest papers in mathematics 2 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 3 first defined by L C Young in Young 1951 4 and proposed them as generalized solutions to Plateau s problem in order to deal with the problem even when a concept of 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 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 Contents 1 Selected publications 2 Notes 3 References 3 1 Biographical references 3 2 General references 3 3 Scientific references 4 See also 5 External linksSelected publications EditAlmgren Frederick J Jr 1964 The theory of varifolds A variational calculus in the large for the k displaystyle k dimensional area integrand Princeton Institute for Advanced Study A set of mimeographed notes in which Frederick J Almgren Jr introduces the term varifold for the first time Almgren Frederick J Jr 1966 Plateau s Problem An Invitation to Varifold Geometry Mathematics Monographs Series 1st ed New York Amsterdam W A Benjamin Inc pp 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 Almgren Frederick J Jr 1999 Taylor Jean E ed Selected works of Frederick J Almgren Jr Collected Works vol 13 Providence R I American Mathematical Society ISBN 978 0 8218 1067 5 MR 1747253 Zbl 0966 01031 Almgren Frederick J Jr 2000 Taylor Jean E Scheffer Vladimir eds Almgren s big regularity paper Q valued functions minimizing Dirichlet s integral and the regularity of area minimizing rectifiable currents up to codimension 2 World Scientific Monograph Series in Mathematics vol 1 River Edge NJ World Scientific Publishing Co Inc ISBN 978 981 02 4108 7 MR 1777737 Zbl 0985 49001 Almgren Frederick J Jr 2001 1966 Plateau s Problem An Invitation to Varifold Geometry Student Mathematical Library vol 13 2nd ed Providence RI American Mathematical Society pp xvi 78 ISBN 978 0 8218 2747 5 MR 1853442 Zbl 0995 49001 The second edition of the book Almgren 1966 Notes Edit According to Almgren s Community of Scholars web site Profile and to Mitchell 1980 p 48 the latter reference lists his appointments at the Institute only up to 1978 Published in book form as Almgren 2000 See his mimeographed notes Almgren 1964 and his book Almgren 1966 the former one is the first exposition of his ideas but the book in both its first and second editions Almgren 2001 had and still has a wider circulation Young calls these geometric objects generalized surfaces in his commemorative papers describing the research of Almgren Brian White 1997 p 1452 footnote 1 1998 p 682 footnote 1 writes that these are essentially the same class of surfaces References EditBiographical references Edit Mitchell Janet A ed 1980 A Community of Scholars Faculty and Members 1930 1980 PDF Princeton New Jersey The Institute for Advanced Study pp xxii 565 archived from the original PDF on 2017 11 07 retrieved 2015 07 04 The New York Times Obituary February 8 1997 Frederick J Almgren Jr 63 Math Professor The New York Times retrieved June 20 2011 The Institute for Advanced Study 2012 Almgren Frederick J Jr A Community of Scholars retrieved 4 July 2015 General references Edit Lieb Elliott H Taylor Jean Morgan Frank Sullivan John Almgren Robert Kusner Robert Marden Albert 1997 Epstein David ed In Memoriam Frederick J Almgren Jr 1933 1997 Experimental Mathematics 6 1 1 12 doi 10 1080 10586458 1997 10504341 MR 1464578 Zbl 0883 01029 Mackenzie Dana 1997 Fred Almgren 1933 1997 lover of mathematics family and life s adventures Notices of the American Mathematical Society 44 9 1102 1106 ISSN 0002 9920 MR 1470170 Zbl 0908 01016 White Brian 1997 The Mathematics of F J Almgren Jr Notices of the American Mathematical Society 44 11 1451 1456 ISSN 0002 9920 MR 1488574 Zbl 0908 01017 White Brian 1998 The mathematics of F J Almgren Jr The Journal of Geometric Analysis 8 5 681 702 doi 10 1007 BF02922665 ISSN 1050 6926 MR 1731057 S2CID 122083638 Zbl 0955 01020 Scientific references Edit Young L C 1951 Surfaces parametriques generalisees Bulletin de la Societe Mathematique de France 79 59 84 doi 10 24033 bsmf 1419 MR 0046421 Zbl 0044 10203 De Giorgi Ennio 1968 Hypersurfaces of minimal measure in pluridimensional euclidean spaces PDF in Petrovsky I G ed Trudy Mezhdunarodnogo kongressa matematikov Proceedings of International Congress of Mathematicians Moscow 1966 ICM Proceedings Moscow Mir Publishers pp 395 401 MR 0234329 Zbl 0188 17503 See also EditAlmgren regularity theorem Almgren Pitts min max theory Almgren Isomorphism TheoremExternal links EditO Connor John J Robertson Edmund F Frederick J Almgren Jr MacTutor History of Mathematics Archive University of St Andrews Frederick J Almgren Jr at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Frederick J Almgren Jr amp oldid 1159455113, wikipedia, wiki, book, books, library,

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