Steven Kerckhoff

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Steven Paul Kerckhoff (* 1952 in Madison, Wisconsin) is an American mathematician who studies hyperbolic manifolds and Teichmüller theory.

Kerckhoff, Stanford 2010

Kerckhoff received his doctorate in 1978 under William Thurston at Princeton University ( The asymptotic geometry of Teichmüller space ). In 1978/79 he was at the Institute for Advanced Study and then at the University of California, Berkeley . He is a professor at Stanford University .

In 1983 he proved a conjecture by Jakob Nielsen (Nielsen Realization Problem). It asks whether a finite subgroup of the mapping class group of a surface can be implemented as an isometric group of a hyperbolic metric on the surface. Kerckhoff proved that this is possible. A previous attempt at evidence by Saul Kravetz in 1959 turned out to be flawed in the 1970s.

He and William Floyd wrote down a large part of the influential lectures (1978/79) of Thurston Geometry and Topology of 3-Manifolds at Princeton.

He dealt with the expansion and establishment of rigorous evidence in the Thurston program, for example regarding the Thurston hyperbolic stretching surgery.

He was invited speaker at the International Mathematicians Congress 1983 in Warsaw . In 1984 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ).

He is also active in math education for schools in California.

Michael Wolf is one of his doctoral students .

Fonts

  • The geometry of Teichmüller space. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 665-678, PWN, Warsaw, 1984.
  • with Daryl Cooper, Craig D. Hodgson Three-dimensional orbifolds and cone-manifolds (with an afterword by Sadayoshi Kojima), Mathematical Society of Japan Memoirs 5th Mathematical Society of Japan, Tokyo, 2000
  • The Nielsen realization problem. Bull. Amer. Math. Soc. (NS) 2 (1980) no. 3, 452-454.
  • The Nielsen realization problem. Ann. of Math. (2) 117 (1983) no. 2, 235-265.
  • with Howard Masur , John Smillie Ergodicity of billiard flows and quadratic differentials , Ann. of Math. (1986) 124: 293-311.
  • with Thurston Noncontinuity of the action of the modular group at Bers' boundary of Teichmüller space , Invent. Math. 100: 25-47 (1990)
  • with Hodgson Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery , J. Differential Geom. 48 (1998), 1-59.
  • with Hodgson: Universal bounds for hyperbolic Dehn surgery. Ann. of Math. (2) 162 (2005) no. 1, 367-421.

Web links

Individual evidence

  1. ↑ Dates of birth according to the Institute for Advanced Study, membership book 1980
  2. ^ Mathematics Genealogy Project
  3. ↑ Nielsen Investigations on the Topology of Closed Two-Sided Surfaces , Part 2, Acta Mathematica, Volume 58, 1932, pp. 87–167
  4. ↑ Kerckhoff The Nielsen realization problem , Annals of Mathematics, Volume 117, 1983, pp. 235-265, announcement in Bulletin AMS, Volume 2, 1980, 452-454
  5. ↑ Partially in expanded form, published in 1997 by Princeton University Press in book form
  6. ^ Thurston in the preface to the lectures
personal data
SURNAME Kerckhoff, Steven
ALTERNATIVE NAMES Kerckhoff, Steven Paul (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH 1952
PLACE OF BIRTH Madison (Wisconsin)