View source for Clifford Taubes

{{short description|American mathematician}}
{{CS1 config|mode=cs2}}
{{BLP sources|date=February 2013}}
{{Infobox scientist
| name              = Clifford Taubes
| image             = Clifford Taubes 2010.jpg
| image_size        = 250px
| caption           = Taubes in 2010.
| birth_date        = {{birth date and age|1954|2|21}}
| birth_place       = New York City, New York
| death_date        = 
| death_place       = 
| nationality       = American
| fields            = [[Mathematical physics]]
| workplaces        = [[Harvard University]]
| alma_mater        = Harvard University
| doctoral_advisor  = [[Arthur Jaffe]]
| doctoral_students = [[Michael Hutchings (mathematician)|Michael Hutchings]]<br />[[Tomasz Mrowka]]
| thesis_title = The Structure of Static Euclidean Gauge Fields
| thesis_year = 1980
| known_for         = [[Taubes's Gromov invariant]]<br>[[Cyclohedron|Bott–Taubes polytope]]
| awards            = [[Shaw Prize]] (2009)<br>[[Clay Research Award]] (2008)<br>[[NAS Award in Mathematics]] (2008)<br>[[Oswald Veblen Prize in Geometry|Veblen Prize]] (1991)
}}
'''Clifford Henry Taubes''' (born February 21, 1954)<ref name=ams1991>{{citation| date=March 1991 | title = 1991 Oswald Veblen Prize in Geometry Awarded in San Francisco  | journal = [[Notices of the American Mathematical Society]]| volume = 38 | issue = 3  | page = 182| url = https://www.ams.org/journals/notices/199103/199103FullIssue.pdf}}</ref> is the William Petschek Professor of Mathematics at [[Harvard University]] and works in [[Gauge theory|gauge field theory]], [[differential geometry]], and low-dimensional [[topology]]. His brother is the journalist [[Gary Taubes]].

==Early career==
Taubes received his B.A. from [[Cornell University]] in 1975 and his Ph.D. in physics in 1980 from [[Harvard University]] under the direction of [[Arthur Jaffe]],<ref name=ams1991/> having proven results collected in {{harvs|last=Jaffe|last2=Taubes|year=1980}} about the existence of solutions to the [[Ginzburg–Landau theory|Landau–Ginzburg]] [[vortex]] equations and the Bogomol'nyi [[monopole (mathematics)|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 equation]]s was used by [[Simon Donaldson]] in his proof of [[Donaldson's theorem]] on diagonizability of [[intersection form]]s. He proved in {{harv|Taubes|1987}} that '''R'''<sup>4</sup> has an uncountable number of [[smooth structure]]s (see also [[exotic R4|exotic '''R'''<sup>4</sup>]]), and (with [[Raoul Bott]] in {{harvnb|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 {{harvnb|Taubes|2000}}), Taubes proved that, on a closed [[Symplectic geometry|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 {{harvnb|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 operator]]s and some methods from {{harvnb|Taubes|2000}}, Taubes proved the longstanding [[Weinstein conjecture]] for all three-dimensional [[contact manifold]]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 {{harvnb|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 Seiberg–Witten Floer homology is isomorphic to Heegaard Floer homology.

==Honors and awards==

*Four-time speaker at [[International Congress of Mathematicians]] (1986, 1994 (plenary), 1998,<ref>{{citation|author=Taubes, Clifford Henry|chapter=The geometry of the Seiberg–Witten invariants|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II|year=1998|pages=493–504|chapter-url=https://www.elibm.org/ft/10011705000}}</ref> 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 [[United States National Academy of Sciences|National Academy of Sciences]] in 1996.
*[[Clay Research Award]] (2008)
*[[NAS Award in Mathematics]] (2008) from the National Academy of Sciences.<ref name=NASMath>{{citation|title=NAS Award in Mathematics|url=http://www.nasonline.org/site/PageServer?pagename=AWARDS_mathematics|publisher=National Academy of Sciences|access-date=13 February 2011|archive-url=https://web.archive.org/web/20101229195210/http://www.nasonline.org/site/PageServer?pagename=AWARDS_mathematics|archive-date=29 December 2010|url-status=dead}}</ref>
*[[Shaw Prize]] in Mathematics (2009) jointly with [[Simon Donaldson]]

==Selected publications==
===Books===
{{sfn whitelist|CITEREFJaffeTaubes1980|CITEREFTaubes2000|CITEREFTaubes2008}}
* 1980: {{SfnRef inline|Jaffe|Taubes|1980}}(with [[Arthur Jaffe]]) ''Vortices and Monopoles: The Structure of Static Gauge Theories'', Progress in Physics, volume 2, [[Birkhäuser]] {{ISBN|3-7643-3025-2}} {{mr|06144447}}
* 1993: ''The L<sup>2</sup> Moduli Spaces on Four Manifold With Cylindrical Ends'' (Monographs in Geometry and Topology){{ISBN|1-57146-007-1}}
* 1996: ''Metrics, Connections and Gluing Theorems'' (CBMS Regional Conference Series in Mathematics) {{ISBN|0-8218-0323-9}}
* 2000: {{SfnRef inline|Taubes|2000}}(ed. Richard Wentworth) ''Seiberg Witten and Gromov invariants for symplectic 4-manifolds'', First International Press Lecture Series, vol. 2, Somerville, MA: International Press, {{ISBN|1-57146-061-6}}, {{MR|1798809}}
* 2008 [2001]: {{SfnRef inline|Taubes|2008}}''Modeling Differential Equations in Biology'' {{ISBN|0-13-017325-8}}
* 2011: ''Differential Geometry: Bundles, Connections, Metrics and Curvature'', (Oxford Graduate Texts in Mathematics #23) {{ISBN|978-0-19-960587-3}}

===Articles===
*{{citation|mr=0882829|last= Taubes|first= Clifford Henry|title= Gauge theory on asymptotically periodic 4-manifolds|journal=[[Journal of Differential Geometry]]|volume=25|year=1987|issue= 3|pages=363–430|doi=10.4310/jdg/1214440981|doi-access=free}}
*{{citation|mr=0954493|last1=Bott|first1= Raoul|author-link1=Raoul Bott|last2= Taubes|first2= Clifford Henry |title= On the rigidity theorems of Witten|journal=[[Journal of the American Mathematical Society]]|volume=2|year=1989|pages=137–186|doi=10.2307/1990915|jstor=1990915|issue=1|doi-access=free}}
*{{citation|mr=2350473|last= Taubes|first= Clifford Henry|title= The Seiberg-Witten equations and the Weinstein conjecture|journal= [[Geometry & Topology]]|volume=11 |year=2007 |issue= 4|pages= 2117–2202|doi=10.2140/gt.2007.11.2117|arxiv=math/0611007|s2cid= 119680690}}
*{{citation|last= Taubes|first= Clifford Henry|title= Embedded contact homology and Seiberg-Witten Floer cohomology I|journal= [[Geometry & Topology]]| volume=14| issue=5| pages=2497–2581| year=2010|arxiv=0811.3985|mr=2746723|doi=10.2140/gt.2010.14.2497}}
*{{citation|last3= Taubes|first3= Clifford Henry|last1=Kutluhan|first1= Cagatay|last2= Lee |first2=Yi-Jen|title= HF=HM I : Heegaard Floer homology and Seiberg–Witten Floer homology
|journal= Geometry & Topology|year=2020|volume= 24|issue= 6|pages= 2829–2854|doi= 10.2140/gt.2020.24.2829|arxiv=1007.1979|s2cid= 118772589}}

==References==
{{Reflist}}

==External links==
*{{MathGenealogy |id=18756}}
*[https://www.ams.org/notices/200805/tx080500596p.pdf Profile in the May 2008 Notices of the AMS, marking his receipt of the NAS Award in Mathematics]

{{Shaw Prize}}
{{Veblen Prize recipients}}

{{Authority control}}

{{DEFAULTSORT:Taubes, Clifford}}
[[Category:1954 births]]
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Clay Research Award recipients]]
[[Category:Harvard University alumni]]
[[Category:Harvard University Department of Mathematics faculty]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:American topologists]]
[[Category:Scientists from Rochester, New York]]
[[Category:Mathematicians from New York (state)]]