# Steven Kerckhoff

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**Steven Paul Kerckhoff** (born 1952) is a [professor](/source/Professor) of [mathematics](/source/Mathematics) at [Stanford University](/source/Stanford_University), who works on [hyperbolic 3-manifolds](/source/Hyperbolic_3-manifold) and [Teichmüller spaces](/source/Teichm%C3%BCller_space).

He received his [Ph.D.](/source/Ph.D.) in mathematics from [Princeton University](/source/Princeton_University) in 1978, under the direction of [William Thurston](/source/William_Thurston). Among his most famous results is his resolution of the [Nielsen realization problem](/source/Nielsen_realization_problem), a 1932 conjecture by [Jakob Nielsen](/source/Jakob_Nielsen_(mathematician)). Along with [William J. Floyd](/source/William_Floyd_(mathematician)), 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](/source/Craig_Hodgson)) in exploring and clarifying Thurston's [hyperbolic Dehn surgery](/source/Hyperbolic_Dehn_surgery).

Kerckhoff is one of four academics from [Stanford University](/source/Stanford_University), along with [Gunnar Carlsson](/source/Gunnar_Carlsson), [Ralph Cohen](/source/Ralph_Louis_Cohen), and [R. James Milgram](/source/R._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. (1983). ["The Nielsen realization problem"](http://projecteuclid.org/euclid.bams/1183546355). *[Annals of Mathematics](/source/Annals_of_Mathematics)*. **117** (2): 235–265. 2nd series. [doi:10.2307/2007076](https://doi.org/10.2307/2007076). [JSTOR 2007076](https://www.jstor.org/stable/2007076). MR 0690845.
- Kerckhoff, Steven P.; [Thurston, William P.](/source/William_Thurston), *Noncontinuity of the action of the modular group at Bers' boundary of Teichmüller space.* [Inventiones Mathematicae](/source/Inventiones_Mathematicae) **100** (1990), no. 1, 25–47.
- Kerckhoff, Steven; Masur, Howard; Smillie, John, *Ergodicity of billiard flows and quadratic differentials.* [Annals of Mathematics](/source/Annals_of_Mathematics) (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.* [Journal of Differential Geometry](/source/Journal_of_Differential_Geometry) **48** (1998), no. 1, 1–59.

## References

- *Big Business, Race, and Gender in Mathematics Reform*, by Steven Krantz (ISBN 0-8218-1398-6). - [Excerpt from this book](http://www.csun.edu/~vcmth00m/krantz.html).
- [Letter from Kerckhoff, Wayne Bishop, Jane Friedman, and Yat-Sun Poon](http://www.csun.edu/~vcmth00m/skills.html), to [California State Curriculum Commission](/source/California_State_Curriculum_Commission) and [California State Board of Education](/source/California_State_Board_of_Education), dated November 21, 2000

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