David Gabai is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and the Hughes-Rogers Professor of Mathematics at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. Focused on

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot th ...

and

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...

, he is a leading researcher in those subjects.

Biography

David Gabai received his B.S. in mathematics from

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the mo ...

in 1976 and his Ph.D. in mathematics from

in 1980. Gabai completed his doctoral dissertation, titled "Foliations and genera of links", under the supervision of

William Thurston William Paul Thurston (October 30, 1946August 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 ...

. After positions at

Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

and

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

, Gabai spent most of the period of 1986–2001 at

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, and has been at Princeton since 2001. Gabai was the Chair of the Department of Mathematics at Princeton University from 2012 to 2019.

Honours and awards

In 2004, David Gabai was awarded the

Oswald Veblen Prize in Geometry __NOTOC__ 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. The Veblen Prize is now worth US$5000, and is ...

, given every three years by the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. He was an invited speaker in the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

2010,

Hyderabad Hyderabad ( ; , ) is the capital and largest city of the Indian state of Telangana and the ''de jure'' capital of Andhra Pradesh. It occupies on the Deccan Plateau along the banks of the Musi River (India), Musi River, in the northern part ...

on the topic of

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

. In 2011, he was elected to the

United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

. In 2012, he became a fellow of the

. Gabai was elected as a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 2014.

Work

David Gabai has played a key role in the field of topology of 3-manifolds in the last three decades. Some of the foundational results he and his collaborators have proved are as follows: Existence of

taut foliation A taut object is one under tension. Taut is also a surname, and may refer to: * Bruno Taut (1880–1938), prolific German architect, urban planner and author * Max Taut (1884–1967), German architect Taut may also refer to: * Tauț, a commune ...

in 3-manifolds,

Property R Conjecture Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, r ...

, foundation of

essential laminations Essential or essentials may refer to: Biology *Essential amino acid, one that the organism cannot produce by itself Groups and organizations * EQ Media Group, formerly Essential Media Group, a global television production company * Essential M ...

Seifert fiber space A Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S^1-bundle ( circle bundle) over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber spaces, and they account for ...

conjecture, rigidity of homotopy hyperbolic 3-manifolds, weak hyperbolization for 3-manifolds with

genuine lamination Genuine may refer to: Companies * Genuine Parts Company, a Fortune 1000 company that was founded in 1928 * Genuine Scooters, a Chicago-based scooter manufacturer *Genuine Games, a video game company founded in early 2002 Music * ''Genuine'' ...

Smale conjecture The Smale conjecture, named after Stephen Smale, is the statement that the diffeomorphism group of the 3-sphere has the homotopy-type of its isometry group, the orthogonal group O(4). It was proved in 1983 by Allen Hatcher. Equivalent statemen ...

for hyperbolic 3-manifolds, Marden's Tameness Conjecture,

Weeks manifold In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead link. It has volume approximately equal to 0.942 ...

being the minimum volume closed

hyperbolic 3-manifold In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1. It ...

Selected works

* ''Foliations and the topology of 3-manifolds''; I: '' J. Differential Geom.'' 18 (1983), no. 3, 445–503; II: J. Differential Geom. 26 (1987), no. 3, 461–478; III: J. Differential Geom. 26 (1987), no. 3, 479–536. * with U. Oertel: ''Essential laminations in 3-manifolds'', '' Ann. of Math.'' (2) 130 (1989), no. 1, 41–73. * ''Convergence groups are Fuchsian groups'', ''Ann. of Math.'' (2) 136 (1992), no. 3, 447–510. * with G. R. Meyerhoff, N. Thurston: ''Homotopy hyperbolic 3-manifolds are hyperbolic'', ''Ann. of Math.'' (2) 157 (2003), no. 2, 335–431. * with D. Calegari: ''Shrinkwrapping and the taming of hyperbolic 3-manifolds'', '' J. Amer. Math. Soc.'' 19 (2006), no. 2, 385–446. * with G. R. Meyerhoff, P. Milley: ''Minimum volume cusped hyperbolic three-manifolds'', ''J. Amer. Math. Soc.'' 22 (2009), no. 4, 1157–1215.

References

External links

* {{DEFAULTSORT:Gabai, David 1954 births Living people Topologists Princeton University faculty Members of the United States National Academy of Sciences Clay Research Award recipients Fellows of the American Mathematical Society Geometers