Frederick J. Almgren Jr.

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.
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

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 (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.

  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".