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Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
and works in gauge field theory,
differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
, and low-dimensional
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
. His brother is the journalist Gary Taubes.


Early career

Taubes received his B.A. from
Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
in 1975 and his Ph.D. in physics in 1980 from
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
under the direction of Arthur Jaffe, 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 (mathematics), scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of suc ...
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 function, smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähl ...
in his proof of
Donaldson's theorem In mathematics, and especially differential topology and gauge theory (mathematics), gauge theory, Donaldson's theorem states that a definite quadratic form, definite intersection form (4-manifold), intersection form of a Compact space, compact, or ...
on diagonizability of intersection forms. 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 mathematical analysis to be performed on the manifold. Definition A smooth structure on a manifold M ...
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 foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott function ...
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 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 as developed by Peter Kronheimer and Tomasz Mrowka together with some new estimates on the spectral flow of
Dirac operator In mathematics and in quantum mechanics, a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as a Laplacian. It was introduced in 1847 by William Ham ...
s and some methods from , Taubes proved the longstanding Weinstein conjecture 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 (differential geometry), distribution in the tangent bundle satisfying a condition called 'complete non-integrability' ...
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 Seiberg–Witten Floer 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 IMU Abacus Medal (known before ...
(1986, 1994 (plenary), 1998, 2010 (plenary; selected, but did not speak)) * Veblen Prize (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 (The Academy) 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 other ...
in 1995. *Elected to the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, 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 ...
in 1996. * Clay Research Award (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." The original p ...
(2008) from the National Academy of Sciences. * Shaw Prize in Mathematics (2009) jointly with
Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth function, smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähl ...


Selected publications


Books

* 1980: (with Arthur Jaffe) ''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 (parti ...
* 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) * 2000: (ed. Richard Wentworth) ''Seiberg Witten and Gromov invariants for symplectic 4-manifolds'', First International Press Lecture Series, vol. 2, Somerville, MA: International Press, , * 2008 001 ''Modeling Differential Equations in Biology'' * 2011: ''Differential Geometry: Bundles, Connections, Metrics and Curvature'', (Oxford Graduate Texts in Mathematics #23)


Articles

* * * * *


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 Department of Mathematics faculty Members of the United States National Academy of Sciences American topologists Scientists from Rochester, New York Mathematicians from New York (state)