威廉·瑟斯顿1946—2012

瑟斯顿1972年获得加州大学伯克利分校的数学博士学位，早年致力于研究3维流形的叶状结构，在很短的时间内取得了一系列成果，使得这个新兴领域迅速走向成熟。70年代末他开始研究3维双曲流形的分类，提出了著名的几何化猜想：任何3维流形均容许一个几何分解，分解后的“零部件”拥有8种可能的几何结构之一。2003年，俄罗斯数学家佩雷尔曼利用理查德·哈密顿发展出的里奇流技术证明了几何化猜想，作为推论，得到了3维庞加莱猜想的证明，这被公认为是本世纪头10年中最伟大的数学成就。

1992-1997年，他担任美国国家数学科学研究所主任。

William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.

Thurston was a professor of mathematics at Princeton University, University of California, Davis, and Cornell University. He was also a director of the Mathematical Sciences Research Institute.

Early life and education

William Thurston was born in Washington, D.C., to Margaret Thurston (née Martt), a seamstress, and Paul Thurston, an aeronautical engineer. William Thurston suffered from congenital strabismus as a child, causing issues with depth perception. His mother worked with him as a toddler to reconstruct three-dimensional images from two-dimensional ones.

He received his bachelor's degree from New College in 1967 as part of its inaugural class. For his undergraduate thesis, he developed an intuitionist foundation for topology. Taking advantage of New College's liberal attitude towards student living arrangements, Thurston at various times lived in a tent in nearby woods or slept in academic buildings.

Following this, he received a doctorate in mathematics from the University of California, Berkeley, under Morris Hirsch, with a thesis titled Foliations of Three-Manifolds which are Circle Bundles in 1972.

Career

After completing his Ph.D., Thurston spent a year at the Institute for Advanced Study, then another year at the Massachusetts Institute of Technology as an assistant professor.

In 1974, Thurston was appointed a full professor at Princeton University. He returned to Berkeley in 1991 to be a professor (1991-1996) and was also director of the Mathematical Sciences Research Institute (MSRI) from 1992 to 1997. He was on the faculty at UC Davis from 1996 until 2003, when he moved to Cornell University.

Thurston was an early adopter of computing in pure mathematics research. He inspired Jeffrey Weeks to develop the SnapPea computing program.

During Thurston's directorship at MSRI, the institute introduced several innovative educational programs that have since become standard for research institutes.

Research

Foliations

His early work, in the early 1970s, was mainly in foliation theory. His more significant results include:

The proof that every Haefliger structure on a manifold can be integrated to a foliation (this implies, in particular, that every manifold with zero Euler characteristic admits a foliation of codimension one).

The construction of a continuous family of smooth, codimension-one foliations on the three-sphere whose Godbillon–Vey invariants (after Claude Godbillon and Jacques Vey) take every real value. This disproved a prevalent conjecture held by topologists that the Godbillon-Vey invariant had to be an integer value.

With John N. Mather, he gave a proof that the cohomology of the group of homeomorphisms of a manifold is the same whether the group is considered with its discrete topology or its compact-open topology.

Awards and honors

In 1976, Thurston and James Harris Simons shared the Oswald Veblen Prize in Geometry.

Thurston received the Fields Medal in 1982 for "revolutioniz[ing] [the] study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry" and "contribut[ing] [the] idea that a very large class of closed 3-manifolds carry a hyperbolic structure."

In 2005, Thurston won the first American Mathematical Society Book Prize, for Three-dimensional Geometry and Topology.

The prize "recognizes an outstanding research book that makes a seminal contribution to the research literature". He was awarded the 2012 Leroy P. Steele Prize by the American Mathematical Society for seminal contribution to research. The citation described his work as having "revolutionized 3-manifold theory".

Personal life

Thurston met his first wife, Rachel Findley, as members of New College's inaugural class. They had three children: Dylan, Nathaniel, and Emily. Dylan was a MOSP participant (1988–90) and is a mathematician at Boston College. Thurston had two children with his second wife, Julian Muriel Thurston: Hannah Jade and Liam.

Thurston died on August 21, 2012, in Rochester, New York, of a sinus mucosal melanoma that was diagnosed in 2011.