Steven Kerckhoff
Encyclopedia
Steven Paul Kerckhoff is a professor
of mathematics
at Stanford University
, who works on hyperbolic 3-manifold
s and Teichmüller space
s.
He received his Ph.D.
in mathematics from Princeton University
in 1978, under the direction of William Thurston
. Among his most famous results is his resolution of the Nielsen realization problem
, a 1932 conjecture by Jakob Nielsen
. Along with William J. Floyd, he wrote large parts of Thurston's influential Princeton lecture notes, and he is well known for his work (some of which is joint with Craig Hodgson) in exploring and clarifying Thurston's hyperbolic Dehn surgery
.
Kerckhoff is one of four academics from Stanford University
, along with Gunnar Carlsson, Ralph Cohen, and James Milgram, who were instrumental in developing the controversial California Mathematics Academic Content Standards for the State Board of Education.
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...
of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
, who works on hyperbolic 3-manifold
Hyperbolic 3-manifold
A hyperbolic 3-manifold is a 3-manifold equipped with a complete Riemannian metric of constant sectional curvature -1. In other words, it is the quotient of three-dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely and properly discontinuously...
s and Teichmüller space
Teichmüller space
In mathematics, the Teichmüller space TX of a topological surface X, is a space that parameterizes complex structures on X up to the action of homeomorphisms that are isotopic to the identity homeomorphism...
s.
He received his 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 mathematics 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....
in 1978, under the direction of William Thurston
William Thurston
William Paul Thurston is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds...
. Among his most famous results is his resolution of the Nielsen realization problem
Nielsen realization problem
The Nielsen realization problem is a question asked by about whether finite subgroups of mapping class groups can act on surfaces, that was answered positively by .-Statement:...
, a 1932 conjecture by Jakob Nielsen
Jakob Nielsen (mathematician)
Jakob Nielsen was a Danish mathematician known for his work on automorphisms of surfaces. He was born in the village Mjels on the island of Als in North Schleswig, in modern day Denmark. His mother died when he was 3, and in 1900 he went to live with his aunt and was enrolled in the Realgymnasium...
. Along with William J. Floyd, he wrote large parts of Thurston's influential Princeton lecture notes, and he is well known for his work (some of which is joint with Craig Hodgson) in exploring and clarifying Thurston's hyperbolic Dehn surgery
Hyperbolic Dehn surgery
In mathematics, hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold...
.
Kerckhoff is one of four academics from Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
, along with Gunnar Carlsson, Ralph Cohen, and James Milgram, who were instrumental in developing the controversial California Mathematics Academic Content Standards for the State Board of Education.
Selected publications
- Kerckhoff, Steven P., The Nielsen realization problem. Annals of MathematicsAnnals of MathematicsThe Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
(second series) 117(2):235–265, 1983. - Kerckhoff, Steven P.; Thurston, William P., Noncontinuity of the action of the modular group at Bers' boundary of Teichmüller space. Invent. Math. 100 (1990), no. 1, 25–47.
- Kerckhoff, Steven; Masur, Howard; Smillie, John, Ergodicity of billiard flows and quadratic differentials. Ann. of Math. (2) 124 (1986), no. 2, 293–311.
- Cooper, Daryl; Hodgson, Craig D.; Kerckhoff, Steven P. Three-dimensional orbifolds and cone-manifolds. With a postface by Sadayoshi Kojima. MSJ Memoirs, 5. Mathematical Society of Japan, Tokyo, 2000. x+170 pp. ISBN 4-931469-05-1
- Hodgson, Craig D.; Kerckhoff, Steven P., Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery. J. Differential Geom. 48 (1998), no. 1, 1–59.