Robert Wolfe Brooks (Washington, D.C., September 16, 1952 – Montreal, September 5, 2002) was a mathematician known for his work in

spectral geometry Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators. The case of the Laplace–Beltrami operator on a closed Riemannian m ...

, Riemann surfaces, circle packings, and

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

. He received his Ph.D. from Harvard University in 1977; his thesis, ''The smooth cohomology of groups of diffeomorphisms'', was written under the supervision of Raoul Bott. He worked at the University of Maryland (1979–1984), then at the University of Southern California, and then, from 1995, at the Technion in Haifa.

Work

In an influential paper , Brooks proved that the

bounded cohomology Boundedness or bounded may refer to: Economics * Bounded rationality, the idea that human rationality in decision-making is bounded by the available information, the cognitive limitations, and the time available to make the decision * Bounded e ...

of a topological space is

isomorphic In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word is ...

to the bounded cohomology of its

fundamental group In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of ...

Honors

Alfred P. Sloan Alfred Pritchard Sloan Jr. ( ; May 23, 1875February 17, 1966) was an American business executive in the automotive industry. He was a long-time president, chairman and CEO of General Motors Corporation. Sloan, first as a senior executive and lat ...

fellowship *

Guastella fellowship Guastella is an Italian surname. Notable people with the surname include: * Ángel Guastella (1931–2016), Argentine rugby union player * Joseph T. Guastella (born 1965), American retired lieutenant general {{surname Italian-language surnames ...

Selected publications

* * * * ::Reviewer Maung Min-Oo for MathSciNet wrote: "This is a well written survey article on the construction of isospectral manifolds which are not isometric with emphasis on hyperbolic Riemann surfaces of constant negative curvature." *Brooks, Robert, "Form in Topology", The Magicians of Form, ed. by Robert M. Weiss. Laurelhurst Publications, 2003.

References

External links

Memorial page (Technion)
* {{DEFAULTSORT:Brooks, Robert W. 20th-century American mathematicians 21st-century American mathematicians 20th-century American Jews 1952 births 2002 deaths American emigrants to Israel Harvard Graduate School of Arts and Sciences alumni Israeli Jews Israeli mathematicians Academic staff of Technion – Israel Institute of Technology University of Southern California faculty Mathematicians from Washington, D.C. Differential geometers American topologists Sloan Research Fellows 21st-century American Jews