# Robert W. Brooks

Robert W. Brooks (1985)

Robert Wolfe Brooks (Washington, D.C., September 16, 1952 – Montreal, September 5, 2002) was a mathematician known for his work in spectral geometry, Riemann surfaces, circle packings, and differential geometry.

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.[1]

## Work

In an influential paper (Brooks 1981), Brooks proved that the bounded cohomology of a topological space is isomorphic to the bounded cohomology of its fundamental group.[2]

## Selected publications

• Brooks, Robert (1981). "Some remarks on bounded cohomology". Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978). Ann. of Math. Stud. Vol. 97. Princeton, N.J.: Princeton Univ. Press. pp. 53–63. MR 0624804.
• Brooks, Robert (1981). "A relation between growth and the spectrum of the Laplacian". Mathematische Zeitschrift. 178 (4): 501–508. doi:10.1007/BF01174771. MR 0638814. S2CID 122114581.
• Brooks, Robert (1981). "The fundamental group and the spectrum of the Laplacian". Commentarii Mathematici Helvetici. 56 (4): 581–598. doi:10.1007/BF02566228. MR 0656213. S2CID 121175762.
• Brooks, Robert (1988). "Constructing isospectral manifolds". American Mathematical Monthly. 95 (9): 823–839. doi:10.1080/00029890.1988.11972094. MR 0967343.
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."[3]
• Brooks, Robert, "Form in Topology", The Magicians of Form, ed. by Robert M. Weiss. Laurelhurst Publications, 2003.

## References

1. ^ Buser, Peter (2005). "On the mathematical work of Robert Brooks". Geometry, spectral theory, groups, and dynamics. Contemp. Math. Vol. 387. Providence, RI: Amer. Math. Soc. pp. 1–35. ISBN 9780821885642. MR 2179784.
2. ^ Ivanov, Nikolai V. (1987). "Foundations of the theory of bounded cohomology". Journal of Mathematical Sciences. 37 (3): 1090–1115. doi:10.1007/BF01086634. MR 0806562. S2CID 122503635.
3. ^