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Frank Morgan (mathematician)
Encyclopedia
Frank Morgan is an American mathematician
and the Webster Atwell '21 Professor of Mathematics at Williams College
, specialising in geometric measure theory
and minimal surface
s.
He is most famous for proving the double bubble conjecture, that the minimum-surface-area enclosure of two given volumes is formed by three spherical patches meeting at 120-degree angles at a common circle. Morgan is a vice-president-elect of the American Mathematical Society
.
Morgan studied at the Massachusetts Institute of Technology
and Princeton University
, and received his Ph.D. from Princeton in 1977, under the supervision of Frederick J. Almgren, Jr.
. He taught at MIT for ten years before joining the Williams faculty.
has recently announced the award of a three-year $145,445 grant to him. Morgan and his students will research manifolds with density, a generalization of Riemannian manifold
s, long prominent in probability and of rapidly growing interest in geometry. Manifold
s, or topological spaces that are locally Euclidean, can be understood intuitively as surfaces. This work will build on research conducted by Morgan and his students over the summer.
Specifically, Morgan intends to approach this area by studying the isoperimetric problem
for manifolds with density such as Gauss space, the premier example of a manifold with density. Isoperimetric problems, which involve finding a closed curve of fixed length, which encloses the greatest area in the plane, have applications in probability theory, in Riemannian geometry, and in Grigori Perelman
’s proof of the Poincaré conjecture
.
Frank Morgan is also an avid dancer. He gained temporary fame for his work "Dancing the Parkway".
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and the Webster Atwell '21 Professor of Mathematics at Williams College
Williams College
Williams College is a private liberal arts college located in Williamstown, Massachusetts, United States. It was established in 1793 with funds from the estate of Ephraim Williams. Originally a men's college, Williams became co-educational in 1970. Fraternities were also phased out during this...
, specialising in geometric measure theory
Geometric measure theory
In mathematics, geometric measure theory is the study of the geometric properties of the measures of sets , including such things as arc lengths and areas. It uses measure theory to generalize differential geometry to surfaces with mild singularities called rectifiable sets...
and minimal surface
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....
s.
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
.
Morgan studied at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
and Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, and received his Ph.D. from Princeton in 1977, under the supervision of Frederick J. Almgren, Jr.
Frederick J. Almgren, Jr.
Frederick Justin Almgren, Jr. was a mathematician working in geometric measure theory...
. He taught at MIT for ten years before joining the Williams faculty.
Current work
Frank Morgan is the founder of SMALL, one of the largest and best known summer undergraduate Mathematics research programs. The National Science FoundationNational Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
has recently announced the award of a three-year $145,445 grant to him. Morgan and his students will research manifolds with density, a generalization of Riemannian manifold
Riemannian manifold
In Riemannian geometry and the differential geometry of surfaces, a Riemannian manifold or Riemannian space is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, which varies smoothly from point to point...
s, long prominent in probability and of rapidly growing interest in geometry. Manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
s, or topological spaces that are locally Euclidean, can be understood intuitively as surfaces. This work will build on research conducted by Morgan and his students over the summer.
Specifically, Morgan intends to approach this area by studying the isoperimetric problem
Isoperimetric problem
Isoperimetric problem may refer to:* Isoperimetric inequality* Any problem in calculus of variations...
for manifolds with density such as Gauss space, the premier example of a manifold with density. Isoperimetric problems, which involve finding a closed curve of fixed length, which encloses the greatest area in the plane, have applications in probability theory, in Riemannian geometry, and in Grigori Perelman
Grigori Perelman
Grigori Yakovlevich Perelman is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.In 1992, Perelman proved the soul conjecture. In 2002, he proved Thurston's geometrization conjecture...
’s proof of the Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
.
Frank Morgan is also an avid dancer. He gained temporary fame for his work "Dancing the Parkway".