# Bruce Kleiner

**Bruce Alan Kleiner** is an American mathematician, working in differential geometry and topology and geometric group theory.

Bruce Kleiner | |
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Bruce Kleiner in Oberwolfach, 2004 | |

Nationality | American |

Alma mater | University of California, Berkeley |

Awards | NAS Award for Scientific Reviewing (2013)[1] Simons Fellow in Mathematics (2014)[2] |

Scientific career | |

Fields | Mathematics |

Institutions | New York University |

Doctoral advisor | Wu-Yi Hsiang |

He received his Ph.D. in 1990 from the University of California, Berkeley. His advisor was Wu-Yi Hsiang. He is now Professor of Mathematics at New York University.

Kleiner has written expository papers on the Ricci flow. Together with John Lott of the University of Michigan, he filled in details of Grigori Perelman's proof of the Geometrization conjecture (from which the Poincaré conjecture follows) in the years 2003–2006. Theirs was the first publication acknowledging Perelman's accomplishment (in May, 2006), which was shortly followed by similar papers by Huai-Dong Cao and Xi-Ping Zhu (in June) and John Morgan and Gang Tian (in July).

Kleiner found a relatively simple proof of Gromov's theorem on groups of polynomial growth. He also proved the Cartan–Hadamard conjecture in dimension 3.

## References

- "Courant's Kleiner wins National Academy of Sciences Award".
*New York University*. Retrieved 10 January 2016. - "2014 Simons Fellows Awardees: Mathematics".
*Simons Foundation*. Archived from the original on 24 March 2015. Retrieved 10 January 2016.

- Kleiner, Bruce; Lott, John (2008),
*Notes on Perelman's Papers*, p. 5667, arXiv:math.DG/0605667, doi:10.2140/gt.2008.12.2587 - Kleiner, Bruce (2010), "A new proof of Gromov's theorem on groups of polynomial growth" (PDF),
*Journal of the American Mathematical Society*,**23**(3): 815–829, arXiv:0710.4593, Bibcode:2010JAMS...23..815K, doi:10.1090/s0894-0347-09-00658-4