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.
Robert Wolfe Brooks | |
|---|---|
| Born | September 16, 1952 Washington, D.C., United States |
| Died | September 5, 2002 (aged 49) Montreal, Canada |
| Alma mater | Harvard University |
| Known for | Spectral geometry, Riemann surfaces, circle packings, differential geometry |
| Awards | Alfred P. Sloan Fellowship, Guastella Fellowship |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Maryland, University of Southern California, Technion – Israel Institute of Technology |
| Doctoral advisor | Raoul Bott |
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
editIn 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]
Honors
edit- Alfred P. Sloan fellowship
- Guastella fellowship
Selected publications
edit- 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
edit- ^ 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.
- ^ 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.
- ^ MR967343