Frederick J. Almgren Jr. Explained

Frederick Justin Almgren
Birth Date:	July 3, 1933
Birth Place:	Birmingham, Alabama, U.S.
Death Place:	Princeton, New Jersey, U.S.
Fields:	Geometric measure theory
Workplaces:	Princeton University
Alma Mater:	Brown 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
Known For:	Plateau's problem, theory of varifolds, Almgren–Pitts min-max theory
Awards:	Guggenheim Fellowship (1974)

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.^[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,^[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

• . A set of mimeographed notes in which Frederick J. Almgren Jr. introduces the term "varifold" for the first time.
• . The first widely circulated book describing the concept of a varifold and its applications to the Plateau's problem.
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• . The second edition of the book .

References

Biographical references

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General references

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Scientific references

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See also

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

Notes and References

1. According to The Institute for Advanced Study|2012}}|Almgren's Community of Scholars web site Profile and to : the latter reference lists his appointments at the Institute only up to 1978.
2. Published in book form as .
3. See his mimeographed notes and his book : the former one is the first exposition of his ideas, but the book (in both its first and second editions) had and still has a wider circulation.
4. Young calls these geometric objects generalized surfaces: in his commemorative papers describing the research of Almgren, writes that these are "essentially the same class of surfaces".