Current Work
Frank Morgan is the founder of SMALL, one of the largest and best known summer undergraduate Mathematics research programs. The National Science Foundation 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 manifolds, long prominent in probability and of rapidly growing interest in geometry. Manifolds, 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".
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