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 higher le ...

and works in gauge field theory,

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, and low-dimensional

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 ...

. His brother is the journalist

Gary Taubes Gary Taubes (born April 30, 1956) is an American journalist, writer, and low-carbohydrate / high-fat (LCHF) diet advocate. His central claim is that carbohydrates, especially sugar and high-fructose corn syrup, overstimulate the secretion of insu ...

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 th ...

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 In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spac ...

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. He i ...

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 In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the ...

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 intro ...

as developed by

Peter Kronheimer Peter Benedict Kronheimer (born 1963) is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology. He is William Caspar Graustein Professor of Mathematics at Harvard University and former ...

and

Tomasz Mrowka Tomasz Mrowka (born September 8, 1961) is an American mathematician specializing in differential geometry and gauge theory. He is the Singer Professor of Mathematics and former head of the Department of Mathematics at the Massachusetts Institu ...

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 formall ...

s and some methods from , Taubes proved the longstanding

Weinstein conjecture In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the conjecture claims that on a compact contact manifold, its Reeb vector field should carry ...

for all three-dimensional

contact manifold In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution ...

s, 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 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 ...

(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, and ...

in 1995. *Elected to the

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 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 The Maryam Mirzakhani Prize in Mathematics (ex-NAS Award in Mathematics until 2012) is awarded by the U.S. National Academy of Sciences "for excellence of research in the mathematical sciences published within the past ten years." Named after the ...

(2008) from the National Academy of Sciences. *

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

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 ''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)