Jeff Cheeger
| Jeff Cheeger | |
|---|---|
 Jeff Cheeger (left) with H. Blaine Lawson (right) in 2007 | |
| Born |
1 December 1943 Brooklyn, U.S. |
| Residence | United States |
| Nationality | American |
| Fields | Mathematician |
| Institutions |
New York University Stony Brook University University of Michigan |
| Alma mater |
Harvard Princeton |
| Doctoral advisor |
Salomon Bochner James Harris Simons |
| Doctoral students |
Xian-Zhe Dai Xiaochun Rong Christina Sormani DaGang Yang Shun-Hui Zhu |
| Known for | Riemannian geometry Metric Geometry |
| Notable awards |
Guggenheim Fellowship(1984) NAS member (1997) Veblen Prize (2001) |
Jeff Cheeger (born December 1, 1943, Brooklyn, New York City), is a mathematician. Cheeger is professor at the Courant Institute of Mathematical Sciences at New York University in New York City. His main interests are differential geometry and its connections with topology and analysis.
Biography
He graduated from Harvard University with a B.A. in 1964. He graduated from Princeton University with an M.S. in 1966 and with a Ph.D. in 1967. He is a Silver Professor at the Courant Institute at NYU where he has worked since 1993.
He worked as a teaching assistant and research assistant at Princeton from 1966–1967, an N.S.F. Postdoctoral Fellow and Instructor from 1967–1968, an assistant professor from 1968 to 1969 at the University of Michigan, and an associate professor from 1969-1971 at SUNY at Stony Brook. Cheeger was a professor at SUNY, Stony Brook from 1971 to 1985, a leading professor from 1985 to 1990, and a distinguished professor from 1990 until 1992.
Cheeger has also had a number of visiting positions in Brazil (1971), at the Institute for Advanced Study (1972, 1977, 1978, 1995), Harvard University (1972), the Institut des Hautes Études Scientifiques (1984–1985) and the Mathematical Sciences Research Institute (1985).
He has supervised at least 13 doctoral theses and three postdocs. He has served as a member of several AMS committees and NSF panels.
Cheeger delivered Invited Addresses at the International Congress of Mathematicians in 1974 and in 1986.
He received the Guggenheim Fellowship in 1984.[1] In 1998 Cheeger was elected a foreign member of the Finnish Academy of Science and Letters.[2]
Cheeger was elected a member of the United States National Academy of Sciences in 1997.[3] He received the Fourteenth Oswald Veblen Prize in Geometry from the American Mathematical Society in 2001.[4]
Honors and awards
- Fellow of the American Mathematical Society, 2012[5]
- Oswald Veblen Prize in Geometry, 2001
- United States National Academy of Sciences, elected 1997
- Max Planck Research Award, Alexander von Humboldt Society, 1992–1994;
- Guggenheim fellowship, 1984–1985;
- Invited Address, Annual Meeting of AMS, 1978;
- International Congress of Mathematicians, 1974 and 1986;
- Sloan Fellowship, 1971–1973;
- National Science Foundation Postdoctoral Fellow, 1967-1968.
Selected publications
- Cheeger, Jeff; Kleiner, Bruce On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces. Inspired by S. S. Chern, 129—152, Nankai Tracts Math., 11, World Sci. Publ., Hackensack, NJ, 2006
- Differentiability of Lipschitz functions on metric measure spaces. Geom. Funct. Anal. 9 (1999), no. 3, 428—517.
- Lower bounds on Ricci curvature and the almost rigidity of warped products, with T. H. Colding. Annals of Math. 144. 1996. 189-237.
- On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay, with G. Tian. Invent Math, 118. 1994. 493-571.
- Collapsing Riemannian manifolds while keeping their curvature bounded, II, with M. Gromov. J. Differential Geometry. 31, 4. 1990. 269-298. Collapsing manifold
- Eta-invariants and their adiabatic limits, with J. M. Bismut. J. American Mathematical Society, 2, 1. 1989. 33-70.
- Cheeger, Jeff; Gromov, Mikhail; Taylor, Michael Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differential Geom. 17 (1982), no. 1, 15—53.
- On the Hodge theory of Riemannian pseudomanifolds. Amer. Soc. Proc. Sym. Pure Math, 36. 1980. 91-146. L² cohomology
- Cheeger, Jeff (1977), "Analytic Torsion and Reidemeister Torsion", PNAS, 74 (7): 2651–2654, doi:10.1073/pnas.74.7.2651, MR 0451312, PMC 431228
, PMID 16592411 Analytic torsion
- Cheeger, Jeff; Gromoll, Detlef The splitting theorem for manifolds of nonnegative Ricci curvature. J. Differential Geometry 6 (1971/72), 119—128. Splitting theorem
- A lower bound for the smallest eigenvalue of the Laplacian. Problems in analysis (Papers dedicated to Salomon Bochner, 1969), pp. 195–199. Princeton Univ. Press, Princeton, N. J., 1970. Cheeger constant
- Cheeger, Jeff; Gromoll, Detlef The structure of complete manifolds of nonnegative curvature. Bull. Amer. Math. Soc. 74 1968 1147—1150. Soul theorem
- Cheeger, Jeff Finiteness theorems for Riemannian manifolds. Amer. J. Math. 92 1970 61—74
- Cheeger, Jeff; Ebin, David G.: Comparison theorems in Riemannian geometry. Revised reprint of the 1975[7] original. AMS Chelsea Publishing, Providence, RI, 2008.
See also
References
- ↑ 1984 U.S. and Canadian Fellows. John Simon Guggenheim Memorial Foundation. Accessed August 11, 2008
- ↑ Foreign Members. Finnish Academy of Science and Letters. Accessed August 11, 2008.
- ↑ NAS Membership Directory. United States National Academy of Sciences. Accessed August 11, 2008. Election citation:"Cheeger has discovered many of the deepest results in Riemannian geometry, such as estimates for the spectrum of the Laplace-Beltrami operator, and the identity of the analytic and geometric definitions of torsion, and has led to the solution of problems in topology, graph theory, number theory, and Markov processes."
- ↑ Fourteenth Veblen Prize, 2001. American Mathematical Society. Accessed August 11, 2008.
- ↑ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
- ↑ <http://as.nyu.edu/object/JeffCheeger.html>
- ↑ Hermann, Robert (1976). "Review: Comparison theorems in Riemannian geometry". Bull. Amer. Math. Soc. 82 (6): 834–836. doi:10.1090/s0002-9904-1976-14175-4.
- ↑ mathscinet