Frederick Justin Almgren Jr. (July 3, 1933 – February 5, 1997) was an Americanmathematician working ingeometric measure theory. He was born in Birmingham, Alabama.

Almgren received aGuggenheim Fellowship in 1974. Between 1963 and 1992 he was a frequent visiting scholar at theInstitute for Advanced Study in Princeton.^[1]

Almgren wrote one of the longest papers in mathematics,^[2] proving what is now called theAlmgren regularity theorem: the singular set of anm-dimensional mass-minimizing surface has dimension at mostm−2. He also developed the concept ofvarifold,^[3] first defined byL. C. Young in (Young 1951),^[4] and proposed them asgeneralized solutions toPlateau's problem in order to deal with the problem even when a concept oforientation is missing. He played also an important role in the founding ofThe Geometry Center.

Almgren was a student ofHerbert Federer, one of the founders ofgeometric measure theory, and was the advisor and husband (as his second wife) ofJean 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.

• Almgren, Frederick J. Jr. (1964),The theory of varifolds: A variational calculus in the large for the${\displaystyle k}$-dimensional area integrand,Princeton:Institute for Advanced Study. A set ofmimeographed 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 thePlateau'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).

• 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 fromthe original(PDF) on 2017-11-07, retrieved2015-07-04.
• The New York Times, Obituary (February 8, 1997),"Frederick J. Almgren Jr., 63, Math Professor",The New York Times, retrievedJune 20, 2011.
• The Institute for Advanced Study (2012),"Almgren, Frederick J. Jr.",A Community of Scholars, retrieved4 July 2015.

• 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.

• Young, L. C. (1951),"Surfaces paramétriques généralisées",Bulletin de la Société Mathématique 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", inPetrovsky, 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, archived fromthe original(PDF) on 2015-07-06, retrieved2015-07-04.

• Almgren regularity theorem
• Almgren–Pitts min-max theory
• Almgren Isomorphism Theorem

• O'Connor, John J.;Robertson, Edmund F.,"Frederick J. Almgren Jr.",MacTutor History of Mathematics Archive,University of St Andrews
• Frederick J. Almgren Jr. at theMathematics Genealogy Project

• 1933 births
• 1997 deaths
• 20th-century American mathematicians
• Institute for Advanced Study visiting scholars
• Princeton University faculty
• Mathematicians from Alabama
• People from Birmingham, Alabama

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• Articles with hCards