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for sale "Deformation Theory" Donald C Spencer Hand Written Letter Dated 1972. 

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Donald

Clayton Spencer (April

25, 1912 – December 23, 2001) was for work on deformation theory of structures arising

in differential geometry, and on several complex variables from the

point of view of partial differential equations. He was

born in Boulder, Colorado, and educated at the University of Colorado and MIT. 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 deformation of complex structures, which

had some influence on the theory geometry, and the conception of moduli spaces.

He also was led to formulate the d-bar Neumann

 problem, for the

operator {\\displaystyle {\\bar

{\\partial }}} (see complex

differential form) in PDE theory, to extend Hodge equations to the

non-compact case. This is used to show existence theorems for holomorphic functions. He later deformation theory, based on a fresh approach to overdetermined systems of PDEs

(bypassing the Cartan–Kähler ideas based on differential

forms by making an intensive use of jets).

Formulated at the level of various chain complexes, 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 a very broad formulation of the notion of integrability. After

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