# Richard S. Hamilton

Richard Hamilton | |
---|---|

Hamilton in 1982 | |

Born | 1943 (age 76–77) |

Nationality | American |

Alma mater | Yale University Princeton University |

Known for | Ricci flow |

Awards | Shaw Prize (2011) Leroy P. Steele Prize (2009) Clay Research Award (2003) Veblen Prize (1996) |

Scientific career | |

Fields | Mathematics |

Institutions | Cornell University University of California, San Diego Columbia University |

Doctoral advisor | Robert Gunning |

Doctoral students | Martin Lo |

**Richard Streit Hamilton** (born 1943) is Davies Professor of Mathematics at Columbia University.

## Biography[edit]

He received his B.A in 1963 from Yale University and Ph.D. in 1966 from Princeton University. Robert Gunning supervised his thesis. Hamilton has taught at University of California, Irvine, University of California, San Diego, Cornell University, and Columbia University.

Hamilton's mathematical contributions are primarily in the field of differential geometry and more specifically geometric analysis. He is best known for having discovered the Ricci flow and starting a research program that ultimately led to the proof, by Grigori Perelman, of the Thurston geometrization conjecture and the solution of the Poincaré conjecture. In August 2006, Perelman was awarded, but declined, the Fields Medal for his proof, in part citing Hamilton's work as being foundational.

Hamilton was awarded the Oswald Veblen Prize in Geometry in 1996 and the Clay Research Award in 2003. He was elected to the National Academy of Sciences in 1999 and the American Academy of Arts and Sciences in 2003. He also received the AMS Leroy P. Steele Prize for a Seminal Contribution to Research in 2009.

On March 18, 2010, it was announced that Perelman had met the criteria to receive the first Clay Millennium Prize for his proof of the Poincaré conjecture.^{[1]} On July 1, 2010, Perelman turned down the prize, saying that he believes his contribution in proving the Poincaré conjecture was no greater than that of Hamilton, who first suggested a program for the solution.

In June 2011, it was announced that the million-dollar Shaw Prize would be split equally between Hamilton and Demetrios Christodoulou for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.^{[2]} ^{[3]}

## Selected publications[edit]

- Hamilton, Richard S. (1982), "Three-manifolds with positive Ricci curvature",
*Journal of Differential Geometry*,**17**(2): 255–306, ISSN 0022-040X, MR 0664497 - Hamilton, Richard S. (1984), "Four-manifolds with positive curvature operator",
*Journal of Differential Geometry*,**24**(2): 153–179, MR 0862046 - Hamilton, Richard S. (1993), "The Harnack estimate for the Ricci flow",
*Journal of Differential Geometry*,**37**(1): 225–243, doi:10.4310/jdg/1214453430, MR 1198607 - Hamilton, Richard S. (1995), "A compactness property for solutions of the Ricci flow",
*American Journal of Mathematics*,**117**(3): 545–572, doi:10.2307/2375080, JSTOR 2375080, MR 1333936 - Hamilton, Richard S. (1995), "The formation of singularities in the Ricci flow",
*Surveys in Differential Geometry*,**2**: 7–136, MR 1375255 - Hamilton, Richard S. (1997), "Four-manifolds with positive isotropic curvature" (PDF),
*Communications in Analysis and Geometry*,**5**(1): 1–92, doi:10.4310/CAG.1997.v5.n1.a1, MR 1456308 - Hamilton, Richard S. (1999), "Non-singular solutions of the Ricci flow on three-manifolds" (PDF),
*Communications in Analysis and Geometry*,**7**(4): 695–729, doi:10.4310/CAG.1999.v7.n4.a2, MR 1714939

## See also[edit]

## References[edit]

**^**"The Poincaré Conjecture". Archived from the original on 2013-07-27.**^**$500,000 for mathematician who laid Poincaré groundwork**^**Shaw Prize in Mathematical Studies 2011

## External links[edit]

- Richard Hamilton at the Mathematics Genealogy Project
- Richard Hamilton – faculty bio at the homepage of the Department of Mathematics of Columbia University
- Richard Hamilton – brief bio at the homepage of the Clay Mathematics Institute
- 1996 Veblen Prize citation
- Lecture by Hamilton on Ricci flow
- Shaw Prize Autobiography

- 1943 births
- Living people
- Members of the United States National Academy of Sciences
- Differential geometers
- 20th-century mathematicians
- 21st-century mathematicians
- Princeton University alumni
- Yale University alumni
- Columbia University faculty
- Clay Research Award recipients
- Educators from Cincinnati
- Mathematicians from Ohio
- Cornell University faculty
- University of California, San Diego faculty