Jeff Cheeger
Encyclopedia
Jeff Cheeger 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 applications to topology
and analysis
.
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. In 1998 Cheeger was elected a foreign member of the Finnish Academy of Science and Letters
.
Cheeger was elected a member of the United States National Academy of Sciences
in 1997.
He received the Fourteenth Oswald Veblen Prize in Geometry
from the American Mathematical Society
in 2001.
, 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.
Analytic torsion
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Cheeger is professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
at the Courant Institute of Mathematical Sciences at New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
. His main interests are differential geometry and its applications to topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
and analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
.
Biography
He graduated from Harvard UniversityHarvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
with a B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in 1964. He graduated from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
with an M.S.
Master of Science
A Master of Science is a postgraduate academic master's degree awarded by universities in many countries. The degree is typically studied for in the sciences including the social sciences.-Brazil, Argentina and Uruguay:...
in 1966 and with a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
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
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of 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
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
(1971), at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
(1972, 1977, 1978, 1995), Harvard University (1972), the Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques
The Institut des Hautes Études Scientifiques is a French institute supporting advanced research in mathematics and theoretical physics...
(1984–1985) and the Mathematical Sciences Research Institute
Mathematical Sciences Research Institute
The Mathematical Sciences Research Institute , founded in 1982, is an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions...
(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
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in 1974 and in 1986.
He received the Guggenheim Fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
in 1984. In 1998 Cheeger was elected a foreign member of the Finnish Academy of Science and Letters
Finnish Academy of Science and Letters
The Finnish Academy of Science and Letters is a Finnish learned society. It was founded in 1908 as a Finnish-language counterpart of the Swedish-language Finnish Society of Sciences and Letters, which had existed since 1838.- Members :The academy has a total of 328 seats for Finnish members...
.
Cheeger was elected a member of the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1997.
He received the Fourteenth Oswald Veblen Prize in Geometry
Oswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
from the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
in 2001.
Honors and awards
Oswald Veblen Prize in GeometryOswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
, 2001
United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
, elected 1997
Max Planck Research Award, Alexander von Humboldt Society, 1992–1994;
Guggenheim fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
, 1984–1985;
Invited Address, Annual Meeting of AMS, 1978;
International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
, 1974 and 1986;
Sloan Fellowship
Sloan Fellowship
The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This is distinct from the Sloan Fellows in business....
, 1971–1973;
National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
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 manifoldCollapsing manifoldIn Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gn, such that as n goes to infinity the manifold is close to a k-dimensional space, where k In Riemannian geometry, a collapsing or collapsed manifold is an...
- 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 cohomologyL² cohomologyIn mathematics, L2 cohomology is a cohomology theory for smooth non-compact manifolds M with Riemannian metric. It is defined in the same way as de Rham cohomology except that one uses square-integrable differential forms...
Analytic torsion
Analytic torsion
In mathematics, Reidemeister torsion is a topological invariant of manifolds introduced by Kurt Reidemeister for 3-manifolds and generalized to higher dimensions by and ....
- 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 constantCheeger constantIn Riemannian geometry, the Cheeger isoperimetric constant of a compact Riemannian manifold M is a positive real number h defined in terms of the minimal area of a hypersurface that divides M into two disjoint pieces of equal volume...
- Cheeger, Jeff; Gromoll, Detlef The structure of complete manifolds of nonnegative curvature. Bull. Amer. Math. Soc. 74 1968 1147—1150. Soul theoremSoul theoremIn mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Cheeger and Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Meyer...
- 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 original. AMS Chelsea Publishing, Providence, RI, 2008.
See also
- Cheeger boundCheeger boundIn mathematics, the Cheeger bound is a bound of the second largest eigenvalue of the transition matrix of a finite-state, discrete-time, reversible stationary Markov chain. It can be seen as a special case of Cheeger inequalities in expander graphs....
- Cheeger constantCheeger constantIn Riemannian geometry, the Cheeger isoperimetric constant of a compact Riemannian manifold M is a positive real number h defined in terms of the minimal area of a hypersurface that divides M into two disjoint pieces of equal volume...
- soul theoremSoul theoremIn mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Cheeger and Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Meyer...
- splitting theorem
- Collapsing manifoldCollapsing manifoldIn Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gn, such that as n goes to infinity the manifold is close to a k-dimensional space, where k In Riemannian geometry, a collapsing or collapsed manifold is an...