Donald C. Spencer

Donald C. Spencer
Born	Donald Clayton Spencer (1912-04-25)April 25, 1912 Boulder, Colorado,U.S.
Died	December 23, 2001(2001-12-23)(aged 89) Durango, Colorado, U.S.
Alma mater	University of Colorado at Boulder Massachusetts Institute of Technology Trinity College, Cambridge
Known for	Spencer cohomology Kodaira–Spencer map Salem–Spencer set
Awards	Bôcher Memorial Prize(1948) National Medal of Science(1989)
Scientific career
Institutions	Princeton University
Doctoral advisor	J. E. LittlewoodandG.H. Hardy
Doctoral students	Pierre Conner Patrick X. Gallagher Phillip Griffiths Robert Hermann Roger Horn Louis Howard Joseph J. Kohn Suresh H. Moolgavkar

Donald Clayton Spencer(April 25, 1912 – December 23, 2001) was an Americanmathematician,known for work ondeformation theoryof structures arising indifferential geometry,and onseveral complex variablesfrom the point of view ofpartial differential equations.He was born inBoulder, Colorado,and educated at theUniversity of ColoradoandMIT.

Career

He wrote a Ph.D. indiophantine approximationunderJ. E. LittlewoodandG.H. Hardyat theUniversity of Cambridge,completed in 1939. He had positions at MIT andStanfordbefore his appointment in 1950 atPrinceton University.There he was involved in a series of collaborative works withKunihiko Kodairaon thedeformation of complex structures,which had some influence on the theory ofcomplex manifoldsandalgebraic geometry,and the conception ofmoduli spaces.

He also was led to formulate thed-bar Neumann problem,for the operator${\bar {\partial }}$(seecomplex differential form) in PDE theory, to extendHodge theoryand then-dimensionalCauchy–Riemann equationsto the non-compact case. This is used to show existence theorems forholomorphic functions.

He later worked onpseudogroupsand their deformation theory, based on a fresh approach tooverdetermined systemsof PDEs (bypassing the Cartan–Kähler ideas based ondifferential formsby making an intensive use ofjets). Formulated at the level of variouschain complexes,this gives rise to what is now calledSpencer cohomology,a subtle and difficult theory both of formal and of analytical structure. This is a kind ofKoszul complextheory, taken up by numerous mathematicians during the 1960s. In particular a theory forLie equationsformulated byMalgrangeemerged, giving a very broad formulation of the notion ofintegrability.

Legacy

After his death, a mountain peak outside Silverton, Colorado was named in his honor.

See also

• Kodaira–Spencer mapping
• Salem–Spencer set

Publications

• Schaeffer, A. C.;Spencer, D. C. (1950),Coefficient Regions for Schlicht Functions,American Mathematical Society Colloquium Publications, Vol. 35, Providence, R.I.:American Mathematical Society,ISBN978-0-8218-1035-4,MR0037908
• Schiffer, M. M.;Spencer, D. C. (1955),Functionals of Finite Riemann Surfaces,Princeton University Press
• Nickerson, H. K.; Spencer, D. C.; Steenrod, N. E. (1959),Advanced Calculus,Princeton, N.J.: Van NostrandNickerson, H. K.; Spencer, D. C.; Steenrod, Norman Earl (2011).Dover reprint.ISBN978-0-4864-8090-9;pbk{{cite book}}:CS1 maint: postscript (link)
• Kumpera, A.; Spencer, D. C. (1972),Lie Equations: Volume I, General Theory,AM-73, Annals of Mathematical Studies, Princeton University Press,ISBN978-0-6910-8111-3;pbk{{citation}}:CS1 maint: postscript (link)
• Kumpera, A.; Spencer, D. C. (1974),Systems of Linear Partial Differential Equations and Deformation of Pseudogroup Structures,Les Presses de l'Université de Montréal

External links

• "Donald C. Spencer (1912–2001)"(PDF).Notices of the American Mathematical Society.51(1). January 2004.
• Donald C. Spencerat theMathematics Genealogy Project
• O'Connor, John J.;Robertson, Edmund F.,"Donald Clayton Spencer",MacTutor History of Mathematics Archive,University of St Andrews
• "Donald C. Spencer, 89, Pioneering Mathematician, Dies".The New York Times.1 January 2002.