Jack Morava

Jack Morava
Jack and Ellen near the Burgess Shale, 1971
Born	(1944-08-06)6 August 1944
Fields	algebraic topology
Institutions	IAS, Columbia, Steklov Institute, TIFR, Stonybrook, Princeton, Johns Hopkins
Alma mater	Rice University

Jack Johnson Morava is an American homotopy theorist at Johns Hopkins University.

Of Czech and Appalachian descent, he was raised in Texas' lower Rio Grande valley. An early interest in topology was strongly encouraged by his parents. He enrolled at Rice University in 1962 as a physics major, but (with the help of Jim Douglas) entered the graduate mathematics program in 1964. His advisor Eldon Dyer arranged, with the support of Michael Atiyah, a one-year fellowship at the University of Oxford, followed by a year in Princeton at the Institute for Advanced Study.

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 Michael J. Hopkins, Smith, and Devinatz'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.