Richard S. Hamilton

This article is about the American mathematician. For other people named Richard Hamilton, see Richard Hamilton.

Richard Hamilton
Hamilton in 1982
Born	1943 (age 80–81) Cincinnati, Ohio, United States
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

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. 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.

Major publications

• Hamilton, Richard S. Harmonic maps of manifolds with boundary. Lecture Notes in Mathematics, Vol. 471. Springer-Verlag, Berlin-New York, 1975. i+168 pp. doi:10.1007/BFb0087227
• Hamilton, Richard S. The inverse function theorem of Nash and Moser. Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 65–222.
• Hamilton, Richard S. Three-manifolds with positive Ricci curvature. J. Differential Geometry 17 (1982), no. 2, 255–306. doi:10.4310/jdg/1214436922
• Gage, M.; Hamilton, R.S. The heat equation shrinking convex plane curves. J. Differential Geom. 23 (1986), no. 1, 69–96. doi:10.4310/jdg/1214439902
• Hamilton, Richard S. Four-manifolds with positive curvature operator. J. Differential Geom. 24 (1986), no. 2, 153–179. doi:10.4310/jdg/1214440433
• Hamilton, Richard S. The Ricci flow on surfaces. Mathematics and general relativity (Santa Cruz, CA, 1986), 237–262, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, 1988.
• Hamilton, Richard S. A matrix Harnack estimate for the heat equation. Comm. Anal. Geom. 1 (1993), no. 1, 113–126. doi:10.4310/CAG.1993.v1.n1.a6
• Hamilton, Richard S. The Harnack estimate for the Ricci flow. J. Differential Geom. 37 (1993), no. 1, 225–243. doi:10.4310/jdg/1214453430
• Hamilton, Richard S. A compactness property for solutions of the Ricci flow. Amer. J. Math. 117 (1995), no. 3, 545–572. doi:10.2307/2375080
• Hamilton, Richard S. The formation of singularities in the Ricci flow. Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 7–136, Int. Press, Cambridge, MA, 1995. doi:10.4310/SDG.1993.v2.n1.a2
• Hamilton, Richard S. Four-manifolds with positive isotropic curvature. Comm. Anal. Geom. 5 (1997), no. 1, 1–92. doi:10.4310/CAG.1997.v5.n1.a1

See also

• Earle–Hamilton fixed-point theorem
• Gage–Hamilton–Grayson theorem
• Yamabe flow

External links

• 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