Frederick J. Almgren Jr.

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.
Died	February 5, 1997(1997-02-05) (aged 63) Princeton, New Jersey, U.S.
Alma mater	Brown University
Known for	Plateau's problem, theory of varifolds, Almgren–Pitts min-max theory
Spouse	Jean Taylor
Awards	Guggenheim Fellowship (1974)
Scientific career
Fields	Geometric measure theory
Institutions	Princeton University
Doctoral advisor	Herbert Federer
Notable students	Robert V. Kohn Frank Morgan Harold R. Parks Jon T. Pitts John M. Sullivan Jean Taylor Brian White

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 ${\displaystyle k}$-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

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), 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

• 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

• 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", 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, archived from the original (PDF) on 2015-07-06, retrieved 2015-07-04.

See also

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

External links

• 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 the Mathematics Genealogy Project