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Clifford Taubes

clifford taubes, clifford taubes harvard math daughter
Clifford Henry Taubes born 1954 is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional 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 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 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 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 has transformed mathematicians' understanding of the topology of symplectic four-manifolds

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 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 Taubes 2008 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 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 0-13-017325-8
  • The L Squared Moduli Spaces on Four Manifold With Cylindrical Ends Monographs in Geometry and TopologyISBN 1-57146-007-1
  • Metrics, Connections and Gluing Theorems CBMS Regional Conference Series in Mathematics ISBN 0-8218-0323-9
  • 2011: Differential Geometry: Bundles, Connections, Metrics and Curvature, Oxford Graduate Texts in Mathematics #23 ISBN 978-0-19-960587-3

References

  1. ^ "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 3-7643-3025-2, 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 4-manifolds, First International Press Lecture Series, 2, Somerville, MA: International Press, pp vi+401, ISBN 1-57146-061-6, MR 1798809 
  • Taubes, Clifford Henry 2007, "The Seiberg-Witten 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 Seiberg-Witten Floer cohomology I" arXiv:08113985  
  • Taubes, Clifford Henry; Kutluhan, Cagatay; Lee, Yi-Jen 2010 "HF=HM I : Heegaard Floer homology and Seiberg--Witten 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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