Frederick Justin Almgren Jr. (July 3, 1933 – February 5, 1997) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

working in

geometric measure theory In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfac ...

. He was born in Birmingham, Alabama. Almgren received a

Guggenheim Fellowship Guggenheim Fellowships are Grant (money), grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon Guggenheim, Simon and Olga Hirsh Guggenheim. These awards are bestowed upon indiv ...

in 1974. Between 1963 and 1992 he was a frequent visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in Princeton. Almgren wrote one of the longest papers in mathematics, proving what is now called the

Almgren regularity theorem In geometric measure theory, a field of mathematics, the Almgren regularity theorem, proved by , states that the singular set of a mass-minimizing surface has codimension at least 2. Almgren's proof of this was 955 pages long. Within the proof man ...

: the singular set of an ''m''-dimensional mass-minimizing surface has dimension at most ''m−2''. He also developed the concept of

varifold In mathematics, a varifold is, loosely speaking, a measure-theoretic generalization of the concept of a differentiable manifold, by replacing differentiability requirements with those provided by rectifiable sets, while maintaining the general alg ...

, first defined by L. C. Young in ,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''". and proposed them as

generalized solution In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some prec ...

s to

Plateau's problem In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem ...

in order to deal with the problem even when a concept of

orientation Orientation may refer to: Positioning in physical space * Map orientation, the relationship between directions on a map and compass directions * Orientation (housing), the position of a building with respect to the sun, a concept in building des ...

is missing. He played also an important role in the founding of ''

The Geometry Center The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. The focus of the center's work was the use of computer ...

''. Almgren was a student of

Herbert Federer Herbert Federer (July 23, 1920 – April 21, 2010) was an American mathematician. He is one of the creators of geometric measure theory, at the meeting point of differential geometry and mathematical analysis.Parks, H. (2012''Remembering Herbert F ...

, one of the founders of

, 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

mimeograph A mimeograph machine (often abbreviated to mimeo, sometimes called a stencil duplicator or stencil machine) is a low-cost duplicating machine that works by forcing ink through a stencil onto paper. The process is called mimeography, and a co ...

ed 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

. *. *. *. The second edition of the book .

Notes

References

Biographical references

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General references

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Scientific references

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External links

* * {{DEFAULTSORT:Almgren, Frederick 1933 births 1997 deaths 20th-century American mathematicians Institute for Advanced Study visiting scholars Princeton University faculty Mathematicians from Alabama People from Birmingham, Alabama