Jack Morava

Jack Johnson Morava (born 6 August 1944) is an American topologist.

Of Czech and Appalachian descent, he was raised in Mercedes, Texas (essentially, in northern Tamaulipas); 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, receiving a Ph.D. in 1968. His thesis adviser was Morton L. Curtis. He subsequently spent a year at Oxford and the Princeton Institute for Advanced Study, where he was mentored by Eldon Dyer and Michael Atiyah. Following a suggestion of the latter, he specialized in relations between K-theory and cobordism, and when Quillen's work on cobordism appeared, he applied it, together with work of Sergei Novikov and Dennis Sullivan, to stable homotopy theory.

In particular, 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 Hopkins, Smith, and Devinatz's proof of 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 multiplicative automorphism groups are essentially the groups of units in certain p-adic division algebras, and thus have interesting connections to local class field theory.

In 1970 he and the linguistic anthropologist Ellen Lee Contini married; they have two children, Aili and Michael. They spent a year at the Steklov Institute in Moscow on a US National Academy of Sciences fellowship, where he was influenced by contact with I. M. Gel’fand, Yuri Manin and Sergei Novikov. He joined the Johns Hopkins University faculty in 1980, where he was later involved in organizing the Japan-US Mathematics Institute. Much of his more recent work involves the application of cobordism categories to mathematical physics, and is posted on the ArXiv; from 2006 to 2010 he was active in DARPA's fundamental questions of biology [1] initiative.

References

• Michael J. Hopkins, Global methods in homotopy theory, in Homotopy theory (Durham, 1985), 73–96, London Math. Soc. Lecture Note Ser., 117, Cambridge Univ. Press, Cambridge, 1987.
• Urs Würgler, Morava K-theories: a survey; in Algebraic topology Poznan 1989, 111–138, Lecture Notes in Math., 1474, Springer, Berlin, 1991.
• Jack Morava at the Mathematics Genealogy Project.
• home page for Jack Morava