View source for Donald C. Spencer

{{short description|American mathematician}}
{{Infobox scientist
| birth_name        = Donald Clayton Spencer
| image             = <!--(filename only)-->
| image_size        = 
| caption           = 
| birth_date        = {{birth date|1912|04|25}}
| birth_place       = [[Boulder, Colorado]], U.S.
| death_date        = {{death date and age|2001|12|23|1912|04|25}}
| death_place       = Durango, Colorado, U.S.
| fields            = 
| workplaces        = [[Princeton University]]
| alma_mater        = [[University of Colorado at Boulder]]<br />[[Massachusetts Institute of Technology]]<br />[[Trinity College, Cambridge]]<ref>Sylvia Nasar, 'Donald C. Spencer, 89, Pioneering Mathematician, Dies', ''[[The New York Times]]'', 1 January 2002. [https://www.nytimes.com/2002/01/01/nyregion/donald-c-spencer-89-pioneering-mathematician-dies.html]</ref>
| doctoral_advisor  = [[J. E. Littlewood]] and [[G.H. Hardy]]
| academic_advisors = 
| doctoral_students = [[Pierre Conner]]<br />[[Patrick X. Gallagher]]<br />[[Phillip Griffiths]]<br />[[Robert Hermann (mathematician)|Robert Hermann]]<br />[[Roger Horn]]<br />[[Louis Howard]]<br />[[Joseph J. Kohn]]<br />[[Suresh H. Moolgavkar]]
| notable_students  = 
| known_for         = [[Spencer cohomology]]<br>[[Kodaira–Spencer map]]<br>[[Salem–Spencer set]]
| author_abbrev_bot = 
| author_abbrev_zoo = 
| influences        = 
| influenced        = 
| awards            = [[Bôcher Memorial Prize]] <small>(1948)</small><br>[[National Medal of Science]] <small>(1989)</small>
| religion          = 
| signature         = <!--(filename only)-->
| footnotes         = 
}}
'''Donald Clayton Spencer''' (April 25, 1912 &ndash; December 23, 2001) was an American [[mathematician]], known for work on [[deformation theory]] of structures arising in [[differential geometry]], and on [[several complex variables]] from the point of view of [[partial differential equation]]s. He was born in [[Boulder, Colorado]], and educated at the [[University of Colorado at Boulder|University of Colorado]] and [[MIT]].

==Career==
He wrote a Ph.D. in [[diophantine approximation]] under [[J. E. Littlewood]] and [[G.H. Hardy]] at the [[University of Cambridge]], completed in 1939. He had positions at MIT and [[Stanford]] before his appointment in 1950 at [[Princeton University]]. There he was involved in a series of collaborative works with [[Kunihiko Kodaira]] on the [[Complex structure deformation|deformation of complex structures]], which had some influence on the theory of [[complex manifold]]s and [[algebraic geometry]], and the conception of [[moduli space]]s.

He also was led to formulate the [[DBAR problem|''d-bar Neumann problem'']], for the operator <math>\bar{\partial}</math> (see [[complex differential form]]) in PDE theory, to extend [[Hodge theory]] and the ''n''-dimensional [[Cauchy–Riemann equations]] to the non-compact case. This is used to show existence theorems for [[holomorphic function]]s.

He later worked on [[pseudogroup]]s and their deformation theory, based on a fresh approach to [[overdetermined system]]s of PDEs (bypassing the Cartan–Kähler ideas based on [[differential form]]s by making an intensive use of [[jet (mathematics)|jets]]). Formulated at the level of various [[chain complex]]es, this gives rise to what is now called [[Spencer cohomology]], a subtle and difficult theory both of formal and of analytical structure. This is a kind of [[Koszul complex]] theory, taken up by numerous mathematicians during the 1960s. In particular a  theory for [[Lie equation]]s formulated by [[Malgrange]] emerged, giving a very broad formulation of the notion of ''integrability''.

==Legacy==
After his death, a mountain peak outside Silverton, Colorado was named in his honor.<ref>{{cite news|last=Pankratz|first=Howard|title=Spencer peak added to Colorado mountain lexicon|url=http://www.denverpost.com/headlines/ci_10237684|access-date=2011-07-23|newspaper=Denver Post|date=2008-08-18}}</ref>

==See also==
*[[Kodaira–Spencer mapping]]
*[[Salem–Spencer set]]

==Publications==

*{{Citation | last1=Schaeffer | first1=A. C. | author-link=Albert Charles Schaeffer | last2=Spencer | first2=D. C. | title=Coefficient Regions for Schlicht Functions | url=https://books.google.com/books?id=9a_wigDUPloC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=American Mathematical Society Colloquium Publications, Vol. 35 | isbn=978-0-8218-1035-4 | mr=0037908  | year=1950}}
*{{Citation | last1=Schiffer | first1=M. M. |author-link=Menahem Max Schiffer | last2=Spencer | first2 = D. C. | title=Functionals of Finite Riemann Surfaces | publisher=[[Princeton University Press]] | year=1955}}<ref>{{cite journal|author=Ahlfors, Lars V.|author-link=Lars Ahlfors|title=Review of ''Functionals of finite Riemann surfaces''. By M. M. Schiffer and D. C. Spencer|journal=Bull. Amer. Math. Soc.|year=1955|volume=61|issue=6|pages=581–584|url=https://www.ams.org/journals/bull/1955-61-06/S0002-9904-1955-09998-1/S0002-9904-1955-09998-1.pdf|doi=10.1090/s0002-9904-1955-09998-1|doi-access=free}}</ref>
*{{Citation | last1=Nickerson | first1=H. K. | last2=Spencer | first2=D. C. | author3=Steenrod, N. E. | title=Advanced Calculus | publisher=Van Nostrand | location=Princeton, N.J. | year=1959}}<ref>{{cite journal|author=Allendoerfer, C. B.|author-link=Carl B. Allendoerfer|title=Review of ''Advanced Calculus''. By H. K. Nickerson, D. C. Spencer and N. E. Steenrod|journal=Bull. Amer. Math. Soc.|year=1960|volume=66|issue=3|pages=148–152|url=https://www.ams.org/journals/bull/1960-66-03/S0002-9904-1960-10411-9/S0002-9904-1960-10411-9.pdf|doi=10.1090/s0002-9904-1960-10411-9|doi-access=free}}</ref>{{cite book|title=Dover reprint|year=2011|isbn=978-0-4864-8090-9|postscript=; pbk|last1=Nickerson|first1=H. K.|last2=Spencer|first2=D. C.|last3=Steenrod|first3=Norman Earl}} 
*{{Citation | last1 = Kumpera | first1=A. | last2 = Spencer | first2=D. C. | title=Lie Equations: Volume I, General Theory | publisher=Princeton University Press | series=AM-73, Annals of Mathematical Studies | isbn=978-0-6910-8111-3 | year=1972 | postscript=; pbk}}
*{{Citation | last1 = Kumpera | first1=A. | last2 = Spencer | first2=D. C. | title=Systems of Linear Partial Differential Equations and Deformation of Pseudogroup Structures | publisher=Les Presses de l'Université de Montréal | year=1974}}

== References ==
{{reflist}}

==External links==
*{{cite journal |title=Donald C. Spencer (1912–2001) |journal=Notices of the American Mathematical Society |volume=51 |issue=1 |date=January 2004 |url=https://www.ams.org/notices/200401/mem-spencer.pdf }}
*{{MathGenealogy |id=10290}}
*{{MacTutor Biography|id=Spencer|title=Donald Clayton Spencer}}
*{{cite news |title=Donald C. Spencer, 89, Pioneering Mathematician, Dies |newspaper=[[The New York Times]] |date=1 January 2002 |url=https://www.nytimes.com/2002/01/01/nyregion/donald-c-spencer-89-pioneering-mathematician-dies.html}}

{{Authority control}}
{{Winners of the National Medal of Science|math-stat-comp}}

{{DEFAULTSORT:Spencer, Donald C.}}
[[Category:1912 births]]
[[Category:2001 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:Alumni of Trinity College, Cambridge]]
[[Category:Massachusetts Institute of Technology alumni]]
[[Category:National Medal of Science laureates]]
[[Category:People from Boulder, Colorado]]
[[Category:Princeton University faculty]]
[[Category:University of Colorado alumni]]