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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.