\"Deformation Theory\" Donald C. Spencer Signed FDC Dated 1963 For Sale

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for sale a RARE! "Deformation Theory" Donald C. Spencer Signed First Day Cover Dated 1963.

ES-9916

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 theory and the n-dimensional Cauchy–Riemann 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.