David Gabai
Encyclopedia
David Gabai, a mathematician
, is currently a professor at Princeton University
. Focused on low-dimensional topology
and hyperbolic geometry
, he is a leading researcher in those subjects.
David Gabai received his S.B. degree from the MIT in 1976 and his Ph.D. from Princeton
in 1980 under the direction of William Thurston
. During his Ph.D., he obtained foundational results on the foliation
s of 3-manifolds; these results are the basis of many research areas in geometric topology
now.
After positions at Harvard and U Penn, he spent most of the years between 1986–2001 at Caltech, and has been at Princeton University
since 2001.
In 2004, David Gabai was awarded the Oswald Veblen Prize in Geometry
, which is one of the most prestigious prizes in geometric topology, given every 3 years by the American Mathematical Society
. In 2011, he was elected to the United States National Academy of Sciences
.
David Gabai has played a key role in the field of topology of 3-manifolds
in the last 3 decades. Some of the foundational results he and his collaborators have proved are as follows: Existence of taut foliation
in 3-manifolds, Property R Conjecture, foundation of essential laminations, Seifert fiber space
conjecture, rigidity of homotopy hyperbolic 3-manifolds, weak hyperbolization for 3-manifolds with genuine lamination, Smale Conjecture for hyperbolic 3-manifolds, Marden's Tameness Conjecture, Weeks's manifold being the minimum volume closed hyperbolic 3-manifold
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, is currently a professor at 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....
. Focused on low-dimensional topology
Low-dimensional topology
In mathematics, low-dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. It can be regarded as a part of geometric topology.A number of...
and hyperbolic geometry
Hyperbolic geometry
In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
, he is a leading researcher in those subjects.
David Gabai received his S.B. degree from the MIT in 1976 and his Ph.D. from Princeton
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....
in 1980 under the direction of William 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...
. During his Ph.D., he obtained foundational results on the foliation
Foliation
In mathematics, a foliation is a geometric device used to study manifolds, consisting of an integrable subbundle of the tangent bundle. A foliation looks locally like a decomposition of the manifold as a union of parallel submanifolds of smaller dimension....
s of 3-manifolds; these results are the basis of many research areas in geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
now.
After positions at Harvard and U Penn, he spent most of the years between 1986–2001 at Caltech, and has been at 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....
since 2001.
In 2004, David Gabai 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...
, which is one of the most prestigious prizes in geometric topology, given every 3 years by the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
. In 2011, he was elected to the United States 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...
.
David Gabai has played a key role in the field of topology of 3-manifolds
3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
in the last 3 decades. Some of the foundational results he and his collaborators have proved are as follows: Existence of taut foliation
Taut foliation
In mathematics, a taut foliation is a codimension 1 foliation of a 3-manifold with the property that there is a single transverse circle intersecting every leaf. By transverse circle, is meant a closed loop that is always transverse to the tangent field of the foliation...
in 3-manifolds, Property R Conjecture, foundation of essential laminations, Seifert fiber space
Seifert fiber space
A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles. In other words it is a S^1-bundle over a 2-dimensional orbifold...
conjecture, rigidity of homotopy hyperbolic 3-manifolds, weak hyperbolization for 3-manifolds with genuine lamination, Smale Conjecture for hyperbolic 3-manifolds, Marden's Tameness Conjecture, Weeks's manifold being the minimum volume closed hyperbolic 3-manifold
Hyperbolic 3-manifold
A hyperbolic 3-manifold is a 3-manifold equipped with a complete Riemannian metric of constant sectional curvature -1. In other words, it is the quotient of three-dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely and properly discontinuously...
.