Clifford Taubes
clifford taubes, clifford taubes harvard math daughterClifford Henry Taubes born 1954 is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and lowdimensional topology His brother, Gary Taubes, is a science writer
Contents
 1 Early career
 2 Work based on Seiberg–Witten theory
 3 Honors and awards
 4 Books
 5 References
 6 External links
Early career
Taubes received his PhD in physics in 1980 under the direction of Arthur Jaffe, having proven results collected in Jaffe & Taubes 1980 about the existence of solutions to the Landau–Ginzburg vortex equations and the Bogomol'nyi monopole equations
Soon, he began applying his gaugetheoretic expertise to pure mathematics His work on the boundary of the moduli space of solutions to the YangMills equations was used by Simon Donaldson in his proof of Donaldson's theorem He proved in Taubes 1987 that R4 has an uncountable number of smooth structures see also exotic R4, and with Raoul Bott in Bott & Taubes 1989 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 2000, Taubes proved that, on a closed symplectic fourmanifold, the gaugetheoretic Seiberg–Witten invariant is equal to an invariant which enumerates certain pseudoholomorphic curves and is now known as Taubes's Gromov invariant This fact has transformed mathematicians' understanding of the topology of symplectic fourmanifolds
More recently in Taubes 2007, 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 operators and some methods from Taubes 2000, Taubes proved the longstanding Weinstein conjecture for all threedimensional 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 Taubes 2008 that a contact 3manifold's embedded contact homology is isomorphic to a version of its Seiberg–Witten Floer cohomology More recently, Taubes, C Kutluhan and YJ Lee proved that embedded contact homology is isomorphic to Heegaard Floer homology
Honors and awards
 Fourtime speaker at International Congress of Mathematicians 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 in 1995
 Elected to the National Academy of Sciences in 1996
 Clay Research Award 2008
 NAS Award in Mathematics 2008 from the National Academy of Sciences[1]
 Shaw Prize in Mathematics 2009 jointly with Simon Donaldson
Books
 Modeling Differential Equations in Biology ISBN 0130173258
 The L Squared Moduli Spaces on Four Manifold With Cylindrical Ends Monographs in Geometry and TopologyISBN 1571460071
 Metrics, Connections and Gluing Theorems CBMS Regional Conference Series in Mathematics ISBN 0821803239
 2011: Differential Geometry: Bundles, Connections, Metrics and Curvature, Oxford Graduate Texts in Mathematics #23 ISBN 9780199605873
References
 ^ "NAS Award in Mathematics" National Academy of Sciences Retrieved 13 February 2011
 Jaffe, Arthur; Taubes, Clifford Henry 1980, Vortices and Monopoles: The Structure of Static Gauge Theories, Progress in Physics, 2, Birkhäuser, ISBN 3764330252, MR 0614447
 Taubes, Clifford Henry 1987, "Gauge theory on asymptotically periodic $4$manifolds", Journal of Differential Geometry, 25: 363–430, doi:104310/jdg/1214440981, MR 0882829
 Bott, Raoul; Taubes, Clifford Henry 1989, "On the rigidity theorems of Witten", Journal of the American Mathematical Society, American Mathematical Society, 2 1: 137–186, doi:102307/1990915, JSTOR 1990915, MR 0954493
 Taubes, Clifford Henry 2000, Wentworth, Richard, ed, Seiberg Witten and Gromov invariants for symplectic 4manifolds, First International Press Lecture Series, 2, Somerville, MA: International Press, pp vi+401, ISBN 1571460616, MR 1798809
 Taubes, Clifford Henry 2007, "The SeibergWitten equations and the Weinstein conjecture", Geometry and Topology, 11: 2117–2202, arXiv:math/0611007 , doi:102140/gt2007112117, MR 2350473
 Taubes, Clifford Henry 2008 "Embedded contact homology and SeibergWitten Floer cohomology I" arXiv:08113985
 Taubes, Clifford Henry; Kutluhan, Cagatay; Lee, YiJen 2010 "HF=HM I : Heegaard Floer homology and SeibergWitten Floer homology" arXiv:10071979
External links
 Clifford Taubes at the Mathematics Genealogy Project
 Profile in the May 2008 Notices of the AMS, marking his receipt of the NAS Award in Mathematics
 

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