Morava brought ideas from
arithmetic geometry into the realm of
algebraic topology. Under Atiyah's tutelage Morava concentrated on the relation between
K-theory and
cobordism, and when
Daniel Quillen's work on that subject appeared he saw that ideas of
Sergei Novikov implied close connections between the
stable homotopy category and the
derived category of
quasicoherent sheaves on the moduli stack of one-dimensional
formal groups; in particular, that the category of spectra is naturally stratified by height. Using work of
Dennis Sullivan, he focused attention on certain
ring spectra parametrized by one-dimensional formal group laws over a field, which generalize classical
topological K-theory. From a modern point of view (i.e., since Ethan Devinatz,
Michael J. Hopkins, and
Jeffrey H. Smith's proof of
Douglas Ravenel's
nilpotence conjecture), it is natural to think of these cohomology theories as the geometric points associated to the prime ideals of the stable homotopy category. Their groups of multiplicative automorphisms are essentially the units in certain p-adic
division algebras, and thus have deep connections to
local class field theory. He joined the
Johns Hopkins University faculty in 1979, and was involved in organizing the Japan-US Mathematics Institute there. Much of his later work involves the application of cobordism categories to mathematical physics, as well as Tannakian descent theory in homotopy categories (posted mostly on the
ArXiv). From roughly 2006 to 2010 he was active in
DARPA's fundamental questions of biology initiative. ==Personal life and death==