Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at

Harvard University 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 high ...

and works in gauge field theory, differential geometry, and low-dimensional

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

. His brother is the journalist Gary Taubes.

Early career

Taubes received his PhD in physics in 1980 under the direction of

Arthur Jaffe Arthur Michael Jaffe (; born December 22, 1937) is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science. Education and career ...

, having proven results collected in about the existence of solutions to the Landau–Ginzburg

vortex In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in ...

equations and the Bogomol'nyi monopole equations. Soon, he began applying his gauge-theoretic expertise to pure mathematics. His work on the boundary of the moduli space of solutions to the Yang-Mills equations was used by

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. H ...

in his proof of

Donaldson's theorem In mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalisable. If the intersection form is positive (ne ...

. He proved in that R⁴ has an uncountable number of

smooth structure In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold. Definition A smooth structure on a manifold M is ...

s (see also exotic R⁴), and (with

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...

in ) proved Witten's rigidity theorem on the elliptic genus.

Work based on Seiberg–Witten theory

In a series of four long papers in the 1990s (collected in ), Taubes proved that, on a closed symplectic four-manifold, the (gauge-theoretic) Seiberg–Witten invariant is equal to an invariant which enumerates certain

pseudoholomorphic curves In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or ''J''-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation. Introduced in 1985 b ...

and is now known as Taubes's Gromov invariant. This fact improved mathematicians' understanding of the topology of symplectic four-manifolds. More recently (in ), by using Seiberg–Witten

Floer homology In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer in ...

as developed by Peter Kronheimer and Tomasz Mrowka together with some new estimates on the spectral flow of

Dirac operator In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian. The original case which concerned Paul Dirac was to factorise forma ...

s and some methods from , Taubes proved the longstanding Weinstein conjecture for all three-dimensional contact manifolds, thus establishing that the Reeb vector field on such a manifold always has a closed orbit. Expanding both on this and on the equivalence of the Seiberg–Witten and Gromov invariants, Taubes has also proven (in a long series of preprints, beginning with ) that a contact 3-manifold's embedded contact homology is isomorphic to a version of its Seiberg–Witten Floer cohomology. More recently, Taubes, C. Kutluhan and Y-J. Lee proved that embedded contact homology is isomorphic to Heegaard Floer homology.

Honors and awards

*Four-time speaker at International Congress of Mathematicians (1986, 1994 (plenary), 1998, 2010 (plenary; selected, but did not speak)) *

Veblen Prize __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 ...

(AMS) (1991) * Elie Cartan Prize (Académie des Sciences) (1993) *Elected as a fellow 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, a ...

in 1995. *Elected to the National Academy of Sciences in 1996. *

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

(2008) * NAS Award in Mathematics (2008) from the National Academy of Sciences. * Shaw Prize in Mathematics (2009) jointly with

Books

* 1980: (with

) ''Vortices and Monopoles: The Structure of Static Gauge Theories'', Progress in Physics, volume 2,

Birkhäuser Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (particu ...

* 1993: ''The L² Moduli Spaces on Four Manifold With Cylindrical Ends'' (Monographs in Geometry and Topology) * 1996: ''Metrics, Connections and Gluing Theorems'' (CBMS Regional Conference Series in Mathematics) * 2008

001 001, O01, or OO1 may refer to: *1 (number), a number, a numeral *001, fictional British agent, see 00 Agent *001, former emergency telephone number for the Norwegian fire brigade (until 1986) *AM-RB 001, the code-name for the Aston Martin Valkyrie ...

''Modeling Differential Equations in Biology'' * 2011: ''Differential Geometry: Bundles, Connections, Metrics and Curvature'', (Oxford Graduate Texts in Mathematics #23)

References

* * * * * *

External links

*
Profile in the May 2008 Notices of the AMS, marking his receipt of the NAS Award in Mathematics
{{DEFAULTSORT:Taubes, Clifford 1954 births Living people 20th-century American mathematicians 21st-century American mathematicians Clay Research Award recipients Harvard University alumni Harvard University faculty Members of the United States National Academy of Sciences Topologists Scientists from Rochester, New York Mathematicians from New York (state)