Richard Hamilton (professor)
Encyclopedia
Richard Streit Hamilton (born 1943) is Davies Professor of mathematics
at Columbia University
.
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 UC Irvine, UC 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 suggesting the 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.
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 18 March 2010, it was announced that Perelman had met the criteria to receive the first Clay Millennium Prize
for resolution of the Poincaré conjecture. On July 1, 2010, he 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
Foundation would be split equally between Hamilton and Demetrios Christodoulou
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
.
He received his B.A in 1963 from Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
and Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1966 from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. Robert Gunning
Robert Gunning (mathematician)
Robert Clifford Gunning is a professor of mathematics at Princeton University specializing in complex analysis. He joined the faculty in 1956 and was dean of the faculty from 1989 to 1995. He was Salomon Bochner's dissertation student.-External links:*...
supervised his thesis. Hamilton has taught at UC Irvine, UC San Diego, Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
, and Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
.
Hamilton's mathematical contributions are primarily in the field of differential geometry and more specifically geometric analysis
Geometric analysis
Geometric analysis is a mathematical discipline at the interface of differential geometry and differential equations. It includes both the use of geometrical methods in the study of partial differential equations , and the application of the theory of partial differential equations to geometry...
. He is best known for having discovered the Ricci flow
Ricci flow
In differential geometry, the Ricci flow is an intrinsic geometric flow. It is a process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric....
and suggesting the research program that ultimately led to the proof, by Grigori Perelman
Grigori Perelman
Grigori Yakovlevich Perelman is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.In 1992, Perelman proved the soul conjecture. In 2002, he proved Thurston's geometrization conjecture...
, of the Thurston
William Thurston
William Paul Thurston is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds...
geometrization conjecture
Geometrization conjecture
Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces...
and the solution of the Poincaré conjecture. In August 2006, Perelman was awarded, but declined, the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
for his proof.
Hamilton was awarded the Oswald Veblen Prize in Geometry
Oswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
in 1996 and the Clay Research Award
Clay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
in 2003. He was elected to the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1999 and the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 2003. He also received the AMS Leroy P. Steele Prize for a Seminal Contribution to Research in 2009.
On 18 March 2010, it was announced that Perelman had met the criteria to receive the first Clay Millennium Prize
Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of September 2011, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize being awarded by the institute...
for resolution of the Poincaré conjecture. On July 1, 2010, he 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
Shaw Prize
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...
Foundation would be split equally between Hamilton and Demetrios Christodoulou
Demetrios Christodoulou
Demetrios Christodoulou is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime...
.
Selected publications
| year=1982 | journal=Journal of Differential Geometry | issn=0022-040X | volume=17 | issue=2 | pages=255–306}} The paper that introduced Ricci flow..External links
- 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 InstituteClay Mathematics InstituteThe Clay Mathematics Institute is a private, non-profit foundation, based in Cambridge, Massachusetts. The Institute is dedicated to increasing and disseminating mathematical knowledge. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998...
- 1996 Veblen Prize citation
- Lecture by Hamilton on Ricci flow